Graduate School of Science and Engineering Mathematics Physics and Earth Sciences Professor |

Last Updated :2021/01/05

- Daisuke Kadoh, Takeru Kamei, Hiroto SoPROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS 2019 (6) 063B04 2019/06 [Peer-reviewed]

Scientific journalWe study a cyclic Leibniz rule, which provides a systematic approach to

lattice supersymmetry, using a numerical method with a transfer matrix. The

computation is carried out in N=2 supersymmetric quantum mechanics with the

phi^6-interaction for weak and strong couplings. The computed energy spectra

and supersymmetric Ward-Takahashi identities are compared with those obtained

from another lattice action. We find that a model with the cyclic Leibniz rule

behaves similarly to the continuum theory compared with the other lattice

action. - Mitsuhiro Kato, Makoto Sakamoto, Hiroto SoPROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS 2018 (12) 121B01 2018/12 [Peer-reviewed]

Scientific journalWe construct N=2 supersymmetric SYK model on one-dimensional (euclidean time)

lattice. One nilpotent supersymmetry is exactly realized on the lattice in use

of the cyclic Leibniz rule (CLR). - Mitsuhiro Kato, Makoto Sakamoto, Hiroto SoPROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS 2017 (4) 043B09 2050-3911 2017/04 [Peer-reviewed]

Scientific journalThe N = 4 supersymmetric quantum mechanical model is formulated on the lattice. Two supercharges, among four, are exactly conserved with the help of the cyclic Leibniz rule without spoiling the locality. In using the cohomological argument, any possible local terms of the effective action are classified into two categories that we call type-I and type-II, analogous to the D- and F-terms in the supersymmetric field theories. We prove a non-renormalization theorem on the type-II terms, which include mass and interaction terms keeping a lattice constant finite, while type-I terms such as the kinetic terms have non-trivial quantum corrections. - Mitsuhiro Kato, Makoto Sakamoto, Hiroto So2014/11We propose a lattice model of supersymmetric complex quantum mechanics which

realizes the non-renormalization theorem on a lattice. In our lattice model,

the Leibniz rule in the continuum, which cannot hold on a lattice due to a

no-go theorem, is replaced by the cyclic Leibniz rule (CLR) for difference

operators. It is shown that CLR allows two of four supercharges of the

continuum theory to preserve while a naive lattice model can realize one

supercharge at the most. A striking feature of our lattice model is that there

are no quantum corrections to potential terms in any finite order of

perturbation theory. This is one of characteristic properties of supersymmetric

theories in the continuum. It turns out that CLR plays a crucial role in the

proof of the non-renormalization theorem. This result suggests that CLR grasps

an essence of supersymmetry on a lattice. - Hiroto So, Kazunori TakenagaPHYSICAL REVIEW D 88 (1) 016001 1550-7998 2013/07 [Peer-reviewed]

Scientific journalWe introduce a four-dimensional cutoff in the scenario of gauge-Higgs unification to control the ultraviolet behavior. A one-loop effective potential for a Higgs field and the Higgs mass are obtained with the cutoff. We find an interrelation between the four-dimensional cutoff and the scale of extra dimensions, which is concretized through the Higgs mass. Combining this interrelation and the recently discovered Higgs boson at the LHC, we obtain an interesting constraint for the four-dimensional cutoff and the extra-dimensional scale. - Mitsuhiro Kato, Makoto Sakamoto, Hiroto SoJOURNAL OF HIGH ENERGY PHYSICS 1305 (5) 089 1029-8479 2013/05 [Peer-reviewed]

Scientific journalIt is old folklore that the violation of Leibniz rule on a lattice is an obstruction for constructing a lattice supersymmetric model. While it is still true for full supersymmetry, we show that a slightly modified form of the Leibniz rule, which we call cyclic Leibniz rule (CLR), is actually a criterion for the existence of partial lattice supersymmetry. In one dimension, we find sets of lattice difference operator and field multiplication smeared over lattice which satisfy the CLR under some natural assumptions such as translational invariance and locality. Thereby we construct a model of supersymmetric lattice quantum mechanics without spoiling locality. The CLR relation is coincident with the condition that the vanishing of the so-called surface term in the construction by lattice Nicolai map. We can construct superfield formalism with arbitrary superpotential. This also enables us to apply safely a localization technique to our model, because the kinetic term and the interaction terms of our model are independently invariant under the supersymmetry transformation. A preliminary attempt in finding a solution for the higher dimensional case is also discussed. - Kouhei Ishiyama, Michika Murata, Hiroto So, Kazunori TakenagaPROGRESS OF THEORETICAL PHYSICS 123 (2) 257 - 269 0033-068X 2010/02 [Peer-reviewed]

Scientific journalIn the framework of a pure SU(2) lattice gauge-Higgs unification scenario, we find a. new global symmetry on a Z(2)-orbifolded five-dimensional space. The global symmetry is consistently realized with the Z(2)-orbifolding, independent of the bulk gauge symmetry. It is shown that the vacuum expectation value of a Z(2)-projected Polyakov loop is a good order parameter for the new symmetry. The effective theory on lattice is also discussed. - Mitsuhiro Kato, Makoto Sakamoto, Hiroto SoJOURNAL OF HIGH ENERGY PHYSICS 0805 (5) 057 1029-8479 2008/05 [Peer-reviewed]

Scientific journalWe study a product rule and a difference operator equipped with Leibniz rule in a general framework of lattice field theory. It is shown that the difference operator can be determined by the product rule and some initial data through the Leibniz rule. This observation leads to a no-go theorem that it is impossible to construct any difference operator and product rule on a lattice with the properties of (i) translation invariance, (ii) locality and (iii) Leibniz rule. We present a formalism to overcome the difficulty by an infinite flavor extension or a matrix expression of a lattice field theory. - Morio Hatakeyama, Hideyuki Sawanaka, Hiroto SoPROGRESS OF THEORETICAL PHYSICS 117 (4) 715 - 728 0033-068X 2007/04 [Peer-reviewed]

Scientific journalTo obtain a light mode in two-dimensional staggered fermions, we introduce four new local operators that preserve the rotational invariance for a staggered Dirac operator. To split the masses of tastes, three cases are considered. The mass matrix and the propagator for free theories are analyzed. We find that one of the three cases may allow the identification of a single mode through the mass splitting. In this case, it is possible that a heavy mode acquires an infinite mass on even sites or odd sites. - Hiroto So, Masashi Hayakawa, Hiroshi SuzukiPoSLAT2006:047,2006 2006/10On a lattice, we construct an overlap Dirac operator which describes the propagation of a Dirac fermion in external gravity. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while the general coordinate invariance is expected to be restored only in the continuum limit. The lattice index density in the presence of a gravitational field is calculated.
- Y Igarashi, M Ishikake, K Itoh, H Sawanaka, H SoJOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 39 (25) 8023 - 8033 0305-4470 2006/06 [Peer-reviewed]

Scientific journalThe infra-red cutoff used in the Wilsonian RG is often incompatible with standard realization of symmetries. We consider a new realization of the chiral symmetry in a fermionic self-interacting system with a regularization that breaks the symmetry. The cutoff dependent symmetry is characterized by the master equation in the Batalin-Vilkovisky antifield formalism. We also explain how the Polchinski RG flow equation respects symmetries. In particular, we discuss the properties of the Polchinski equation under the cutoff dependent chiral symmetry. - Masashi Hayakawa, Hiroto So, Hiroshi SuzukiPROGRESS OF THEORETICAL PHYSICS 116 197 - 215 2006/04 [Peer-reviewed]

Scientific journalWe construct a lattice Dirac operator of overlap type that describes the propagation of a Dirac fermion in an external gravitational field. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while it is believed that the general coordinate invariance is restored only in the continuum limit. Our doubler-free Dirac operator satisfies the conventional Ginsparg-Wilson relation and possesses gamma_5 hermiticity with respect to the inner product, which is suggested by the general coordinate invariance. The lattice index theorem in the presence of a gravitational field holds, and the classical continuum limit of the index density reproduces the Dirac genus. Reduction to a single Majorana fermion is possible for 8k+2 and 8k+4 dimensions, but not for 8k dimensions, which is consistent with the existence of the global gravitational/gauge anomalies in 8k dimensions. Other Lorentz representations, such as the spinor-vector and the bi-spinor representations, can also be treated. Matter fields with a definite chirality (with respect to the lattice-modified chiral matrix) are briefly considered. - Hiroto So, Hiroshi SuzukiPROGRESS OF THEORETICAL PHYSICS 115 467 - 471 2005/11 [Peer-reviewed]

Scientific journalA zero-dimensional analogue of Witten's global gauge anomaly is considered. For example, a zero-dimensional reduction of the two-dimensional $\SO(2N)$ Yang-Mills theory with a single Majorana-Weyl fermion in the fundamental representation suffers from this anomaly. Another example is a zero-dimensional reduction of two- and three-dimensional $\SU(2N_c)$ Yang-Mills theories which couple to a single Majorana fermion in the adjoint representation. In this case, any expectation value is either indeterminate or infinite. - K Itoh, M Kato, M Murata, H Sawanaka, H SoPROGRESS OF THEORETICAL PHYSICS 114 (3) 631 - 641 0033-068X 2005/09 [Peer-reviewed]

Scientific journalWe present a new formulation of a staggered fermion on a D-dimensional lattice based on the SO(2D) Clifford algebra, which is naturally contained in the action. The action of a massless staggered fermion is invariant under discrete rotations and SO(2D) chiral and other discrete transformations. From the transformation properties of the fermion, we find two local meson operators (one scalar and one pseudoscalar), in addition to two standard meson operators. - K Itoh, M Kato, M Murata, H Sawanaka, H SoNUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS 140 769 - 771 0920-5632 2005/03 [Peer-reviewed]

Scientific journalWe investigate exact symmetries of a staggered fermion in D dimensions. The Dirac operator is reformulated by SO(2D) Clifford algebra. The chiral symmetry, rotational invariance and parity symmetries are clarified in any dimension. Local scalar and pseudo-scalar modes are definitely determined, in which we find non-standard modes. The relation to Ichimatsu-patterned lattice approach is discussed. - M Murata, H SoNUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS 129 786 - 788 0920-5632 2004/03 [Peer-reviewed]

Scientific journalA higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. We propose the new possibility to realize the continuum limit of a five-dimensional theory based on the property of the phase diagram. - Y Igarashi, H So, N UkitaNUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS 119 778 - 780 0920-5632 2003/05 [Peer-reviewed]

Scientific journalWe apply the antifield formalism with an auxiliary method to construction of a lattice chiral symmetry in theories with self-interacting fermions. The quantum master equation (QME) of the antifield formalism which leads to Ginsparg-Wilson (GW) relation in interacting theories can be solved in a closed form. These solutions are used, after suitable canonical transformations, to discuss lattice chiral symmetry. - K Itoh, M Kato, M Murata, H Sawanaka, H SoNUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS 119 906 - 908 0920-5632 2003/05 [Peer-reviewed]

Scientific journalWe proposed an 'Ichimatsu'-decomposed lattice gauge theory with fermionic symmetries. The vacuum structures of the gauge sector with two coupling constants (beta(p), beta(c)) are investigated for 3-dimensional Z(2) and 4-dimensional SU(2). cases using mean-field approximation and numerical simulation. We found two phases on the (beta(p), beta(c)) phase diagram for 3-dim. Z(2) case, while the diagram is a single phase for the latter. - K Itoh, M Kato, H Sawanaka, H So, N UkitaNUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS 119 903 - 905 0920-5632 2003/05 [Peer-reviewed]

Scientific journalWe present the lattice models with exact fermionic symmetries relating fermions and link variables. The plaquettes are distributed in an Ichimatsu pattern (chequered). We explain this peculiar structure allows us to have a translation in the algebra of the fermionic symmetries. - K Itoh, M Kato, H Sawanaka, H So, N UkitaJOURNAL OF HIGH ENERGY PHYSICS 0302 (2) 033 1029-8479 2003/02 [Peer-reviewed]

Scientific journalWe present a lattice theory with an exact fermionic symmetry, which mixes the link and the fermionic variables. The staggered fermionic variables may be reconstructed into a Majorana fermion in the continuum limit. The gauge action has a novel structure. Though it is the ordinary plaquette action, two different couplings are assigned in the "Ichimatsu pattern" or the checkered pattern. In the naive continuum limit, the fermionic symmetry survives as a continuum (or an O(a(0))) symmetry. The transformation of the fermion is proportional to the field strength multiplied by the difference of the two gauge couplings in this limit. This work is an extension of our recently proposed cell model toward the realization of supersymmetric Yang-Mills theory on lattice. - Y Igarashi, H So, N UkitaNUCLEAR PHYSICS B 640 (1-2) 95 - 118 0550-3213 2002/09 [Peer-reviewed]

Scientific journalRecently we have discussed realization of an exact chiral symmetry in theories with self-interacting fermions on the lattice, based upon an auxiliary field method. In this paper we describe construction of the lattice chiral symmetry and discuss its structure in more detail. The antifield formalism is used to make symmetry consideration more transparent. We show that the quantum master equation in the antifield formalism generates all the relevant Ward-Takahashi identities including a Ginsparg-Wilson relation for interacting theories. Solutions of the quantum master equation are obtained in a closed form, but the resulting actions are found to be singular. Canonical transformations are used to obtain four types of regular actions. Two of them may define consistent quantum theories. Their Yukawa couplings are the same as those obtained by using the chiral decomposition in the free field algebra. Inclusion of the complete set of the auxiliary fields is briefly discussed. (C) 2002 Elsevier Science B.V. All rights reserved. - K Itoh, M Kato, H Sawanaka, H So, N UkitaPROGRESS OF THEORETICAL PHYSICS 108 (2) 363 - 374 0033-068X 2002/08 [Peer-reviewed]

Scientific journalWe present an entirely new approach toward a realization of supersymmetric Yang-Mills theory on the lattice. The action consists of the staggered fermion and the plaquette variables distributed in the Euclidean spare, with a particular pattern. The system is shown to have fermionic symmetries relating the fermion and link variables. - Y Igarashi, H So, N UkitaPHYSICS LETTERS B 535 (1-4) 363 - 370 0370-2693 2002/05 [Peer-reviewed]

Scientific journalWe derive Ginsparg-Wilson relation for a lattice chiral symmetry in theories with self-interacting fermions. Auxiliary scalar and pseudo-scalar fields are introduced on a coarse lattice to give an effective description of the fermionic interactions. We obtain particular solutions to the Ginsparg-Wilson relation and other Ward-Takahashi identities in a closed form. These non-perturbative solutions can be used to construct a chiral invariant action and an invariant path-integral measure on the coarse lattice. The resulting partition function exhibits the exact chiral symmetry in the fermionic system with the auxiliary fields. (C) 2002 Elsevier Science B.V. All rights reserved. - K Itoh, M Kato, H Sawanaka, H So, N UkitaNUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS 106 947 - 949 0920-5632 2002/03 [Peer-reviewed]

Scientific journalWe present a new lattice super Yang-Mills theory and its SUSY transformation. After our formulation of the model in a fundamental lattice, it is extended to the whole lattice with a substructure of modulo 2. - Y. Igarashi, K. Itoh, H. SoInternational Journal of Modern Physics A 16 (11) 2047 - 2051 0217-751X 2001/04 [Peer-reviewed]

International conference proceedingsWe show that the BRS symmetry is present even with the finite IR cutoff in the Wilsonian RG approach. Based on the antifield formalism, we explain how the symmetry is realized on the RG flow. - M Koseki, H So, N UkitaINTERNATIONAL JOURNAL OF MODERN PHYSICS A 16 (11) 2059 - 2063 0217-751X 2001/04 [Peer-reviewed]

Scientific journal - Yuji Igarashi, Katsumi Itoh, Hiroto SoProgress of Theoretical Physics 104 (5) 1053 - 1066 0033-068X 2000 [Peer-reviewed]

Scientific journalUsing the average action, defined with a continuum analog of the block spin transformation, we demonstrate the presence of a gauge symmetry along the Wilsonian renormalization group flow. As a reflection of this gauge symmetry, the average action satisfies the quantum master equation (QME). We show that the quantum part of the master equation can be naturally understood, once the measure contribution under the BRS transformation is taken into account. Furthermore, an effective BRS transformation acting on macroscopic fields may be defined from the QME. The average action is explicitly evaluated in terms of the saddle point approximation up to one-loop order. It is confirmed that the action satisfies the QME and the flow equation. - H So, N UkitaPHYSICS LETTERS B 457 (4) 314 - 318 0370-2693 1999/06 [Peer-reviewed]

Scientific journalThe Ginsparg-Wilson (GW) relation is extended for supersymmetric free theories on a lattice. Exact lattice supersymmetry (SUSY) can be defined without any ambiguities in difference operators. The lattice action constructed by a block-spin transformation is invariant under the symmetry. U(1)(R) symmetry on the lattice is also realized as one of exact symmetries. For an application, the extended CW relation is given for a two-dimensional model with chiral-multiplets. It is argued that the relation may be generalized for interacting cases. (C) 1999 Published by Elsevier Science B.V. All rights reserved. - EA PASCHOS, U SARKAR, H SOPHYSICAL REVIEW D 52 (3) 1701 - 1705 0556-2821 1995/08 [Peer-reviewed]

Scientific journalIn E(6) models there are new particles whose baryon number is not uniquely assigned. We point out that the baryon and lepton number assignment to these particles can change the baryogenesis scenario significantly. We consider a left-right symmetric extension of the standard model in which the (B - L) quantum number is gauged. The identification of (B - L) with a generator of E(6) is used to define the baryon and lepton numbers for the exotic particles in a way that the electroweak baryon and lepton number anomaly corresponding to the SU(2)(L) group vanishes; i.e., there is no nonperturbative baryon or lepton number violation during the electroweak phase transition. We study some consequences of the new assignment. - VG KISELEV, H SOPHYSICS LETTERS B 342 (1-4) 270 - 276 0370-2693 1995/01 [Peer-reviewed]

Scientific journalWe argue for the existence of an upper bound m* on the Higgs mass at which the lowest excited state of the Higgs field ceases to be the conventional plane wave. An explicit construction of an alternative nonperturbative state is discussed. This excitation is spatially localized. The field fluctuations inside the localization region are large. The energy of the excitation is smaller than the mass of the plane wave state m at m > m*. An approximate value of m* is found to be m* approximate to 4.75 times the vacuum expectation value. This is an upper bound at the tree level. - J BAACKE, H SO, A SURIGZEITSCHRIFT FUR PHYSIK C-PARTICLES AND FIELDS 63 (4) 689 - 695 0170-9739 1994/09 [Peer-reviewed]

Scientific journalWe present results for the fermion determinant in an external Yukawa-coupled scalar field, a quantity relevant to instanton and sphaleron transition rates as well as bubble nucleation occuring in the electroweak phase transition when the scalar field is identified with the Higgs field. We calculate the determinant exactly and find an approximation (essentialy of the gradient expansion type) that reproduces the exact results very well if the fermion mass m(F) becomes larger than the inverse of the size R of the background field configuration. The results are given for 2, 3 and 4 Euclidean dimensions. - H ASANO, H KANADA, H SOMODERN PHYSICS LETTERS A 6 (38) 3499 - 3508 0217-7323 1991/12 [Peer-reviewed]

Scientific journalThe vacuum structure with a non-trivial winding number (the baryon number) of a quantum nonlinear sigma-model is investigated. Some falling paths to the vacuum are found in a finite-dimensional subspace of the infinite-dimensional configuration space. It is also shown by numerical calculation that the anti-baryon density is appeared in the outer region on the way of some paths falling into the vacuum. In addition, we also discuss some configurations without hedgehog ansatz. - H ASANO, H KANADA, H SOPHYSICAL REVIEW D 44 (1) 277 - 288 0556-2821 1991/07 [Peer-reviewed]

Scientific journalWe detail the derivation of the general covariant quantum Hamiltonian for the nonlinear sigma-model by introducing collective coordinates for the quantization of virbrational and rotational modes. The stability of the quantum state in the nonlinear sigma-model is analytically and numerically investigated by the variational treatment of the profile function. We show that in the pure nonlinear sigma-model without a Skyrme term, the stabilization against collapse of the state cannot be achieved with the quantum fluctuation effect of the vibrational mode only, but needs a stabilizing term added to the model Lagrangian. We also find that the Skyrme term is a suitable candidate for the stabilizer. It is shown that there is a stable solution with rotational motion in the Skryme model. The calculated values of the physical quantities (mass, rms radius, and baryon density) for a Skyrmion are given. It is also shown that the present results are very similar to those obtained with the rotating model of the static Skyrme soliton. - Y IGARASHI, H IMAI, S KITAKADO, J KUBO, H SOMODERN PHYSICS LETTERS A 5 (21) 1663 - 1670 0217-7323 1990/08 [Peer-reviewed]

Scientific journal - M SUWA, H SOPROGRESS OF THEORETICAL PHYSICS 83 (2) 274 - 285 0033-068X 1990/02 [Peer-reviewed]

Scientific journal - Y IGARASHI, H IMAI, S KITAKADO, H SOPHYSICS LETTERS B 227 (2) 239 - 244 0370-2693 1989/08 [Peer-reviewed]

Scientific journal - KI AOKI, M BANDO, H MINO, T NONOYAMA, H SO, K YAMAWAKIPROGRESS OF THEORETICAL PHYSICS 82 (2) 388 - 395 0033-068X 1989/08 [Peer-reviewed]

Scientific journal - K FUJII, H SO, M SUWALETTERS IN MATHEMATICAL PHYSICS 15 (2) 151 - 158 0377-9017 1988/02 [Peer-reviewed]

Scientific journal - M BANDO, T MOROZUMI, H SO, K YAMAWAKIPHYSICAL REVIEW LETTERS 59 (4) 389 - 392 0031-9007 1987/07 [Peer-reviewed]

Scientific journal - T MOROZUMI, H SOPROGRESS OF THEORETICAL PHYSICS 77 (6) 1434 - 1449 0033-068X 1987/06 [Peer-reviewed]

Scientific journal - H DATE, K FUJII, H SOLETTERS IN MATHEMATICAL PHYSICS 13 (3) 195 - 200 0377-9017 1987/04 [Peer-reviewed]

Scientific journal **Discriminating Technicolor Theories Through Flavor Changing Neutral Currents: Walking Or Standing Coupling Constants?**Masako Bando, Takuya Morozumi, Hiroto So, Koichi YamawakiPhysical Review Letters 59 389 1987 [Peer-reviewed]

Scientific journal- S MIDORIKAWA, H SO, S YOSHIMOTOZEITSCHRIFT FUR PHYSIK C-PARTICLES AND FIELDS 34 (3) 307 - 312 0170-9739 1987 [Peer-reviewed]

Scientific journal - H SOPROGRESS OF THEORETICAL PHYSICS 74 (3) 585 - 593 0033-068X 1985 [Peer-reviewed]

Scientific journal - H SOPROGRESS OF THEORETICAL PHYSICS 73 (2) 528 - 532 0033-068X 1985 [Peer-reviewed]

Scientific journal - T KASHIWA, H SOPROGRESS OF THEORETICAL PHYSICS 73 (3) 762 - 789 0033-068X 1985 [Peer-reviewed]

Scientific journal

- Numerical analyses of N=2 supersymmetric quantum mechanics with cyclic Leibniz rule on lattice [Not invited]D.Kadoh, T.Kamei, H.So2019 Annual Meeting of Physical Society of Japan in Autumn 2019/09
- Sign problem and CLR [Not invited]SO HirotoShikoku Siminar 2018 2018/12
- Numerical analysis of supersymmetric quantum mechanics on lattice with cyclic Leibniz rule [Not invited]KADOH Diasuke, KAMEI Takeru, SO Hiroto2018 Autumn Meeting of Japan Physical Society 2018/09
- Cohomological property of CLR-realized supersymmetric quantum mechanics on lattice [Not invited]KATO Mitsuhiro, SAKAMOTO Makoto, SO Hiroto2016 Annual Meeting of Japan Physical Society 2016/03
- Mitsuhiro Kato, Makoto Sakamoto, Hiroto SoProceedings of Science 2014/01© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. We propose a lattice model of supersymmetric complex quantum mechanics which realizes the non-renormalization theorem on a lattice. In our lattice model, the Leibniz rule in the continuum, which cannot hold on a lattice due to a no-go theorem, is replaced by the cyclic Leibniz rule (CLR) for difference operators. It is shown that CLR allows two of four supercharges of the continuum theory to preserve while a naive lattice model can realize one supercharge at the most. A striking feature of our lattice model is that there are no quantum corrections to potential terms in any finite order of perturbation theory. This is one of characteristic properties of supersymmetric theories in the continuum. It turns out that CLR plays a crucial role in the proof of the non-renormalization theorem. This result suggests that CLR grasps an essence of supersymmetry on a lattice.
- Mitsuhiro Kato, Makoto Sakamoto, Hiroto SoProceedings of Science 2013/01© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. For the purpose of constructing supersymmetric(SUSY) theories on lattice, we propose a new type relation on lattice -cyclic Leibniz rule(CLR)- which is slightly different from an ordinary Leibniz rule. Actually, we find that CLR can enlarge the number of SUSYs and construct more Nicolai mappings in a quantum-mechanical model. In this model, the exact mass degeneracy between fermion and boson is shown.
- Leibniz rule, locality and supersymmetry on lattice [Not invited]Mitsuhiro Kato, Makoto Sakamoto, Hiroto SoProceedings of Science 2012/01In a finite volume system, we prove a no-go theorem on a Leibniz rule with a care of locality argument on latttice. The new possibility on the Leibniz rule solutions on lattice is discussed. Although the new solution admits a local difference operator, a non-local product rule is needed. In the case, a supersymmetric interacting theory is simply realized. The difference between finite flavor systems and matrix representations of infinite flavor systems is explained based on a finite volume system analysis including the no-go theorem.
- Michika Murata, Hiroto So, Kazunori TakenagaProceedings of Science 2010/01© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. In an SU(2) lattice gauge theory with a Z2 orbifolded extra dimension, the new symmetry which is called as a stick symmetry is useful in understanding the bulk transition. We discuss the relation with the Fradkin-Shenker's phase diagram as well. A remnant of the extra dimension is remained as two U(1) gauge symmetries in two 4-dimensional spaces. We also consider more general bulk gauge groups beyond SU(2).
- Mitsuhiro Kato, Makoto Sakamoto, Hiroto SoPoS LATTICE2008:233,2008 2008/10An obstacle to realize supersymmetry on a lattice is the breakdown of Leibniz rule. We give a proof of a no-go theorem that it is impossible to construct a lattice field theory in an infinite lattice volume with any nontrivial field products and difference operators that satisfy the following three properties: (i) translation invariance, (ii) locality and (iii) Leibniz rule. We then propose a way to escape from the no-go theorem by introducing infinite flavors, and present a lattice model of N=2 supersymmetric quantum mechanics equipped with the full exact supersymmetry.
- Mitsuhiro Kato, Makoto Sakamoto, Hiroto SoProceedings of Science 2008/01© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. An obstacle to realize supersymmetry on a lattice is the breakdown of Leibniz rule. We give a proof of a no-go theorem that it is impossible to construct a lattice field theory in an infinite lattice volume with any nontrivial field products and difference operators that satisfy the following three properties: (i) translation invariance, (ii) locality and (iii) Leibniz rule. We then propose a way to escape from the no-go theorem by introducing infinite flavors, and present a lattice model of N = 2 supersymmetric quantum mechanics equipped with the full exact supersymmetry.
- Overlap Fermion in External Gravity [Not invited]Hiroto So, Masashi Hayakawa, Hiroshi SuzukiPoSLAT2006:047,2006 2006/10On a lattice, we construct an overlap Dirac operator which describes the propagation of a Dirac fermion in external gravity. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while the general coordinate invariance is expected to be restored only in the continuum limit. The lattice index density in the presence of a gravitational field is calculated.
- Leibniz rule and exact supersymmetry on lattice: a case of supersymmetrical quantum mechanics [Not invited]Mitsuhiro Kato, Makoto Sakamoto, Hiroto SoPoS LAT2005 (2005) 274 2005/09We propose a new formulation of lattice theory. It is given by a matrix form and suitable for satisfying Leibniz rule on lattice. The theory may be interpreted as a multi-flavor system. By realizing the difference operator as a commutator, we may obtain exact supersymmetric theories on lattice explicitly. Some problems such as locality and single flavor reduction are also commented.
- Supersymmetry on Lattice Using Ginsparg-Wilson Relation [Not invited]Hiroto. So, Naoya UkitaNucl.Phys.Proc.Suppl. 94 (2001) 795-798 2000/11The Ginsparg-Wilson(G-W) relation for chiral symmetry is extended for a supersymmetrical(SUSY) case on a lattice. It is possible to define exact lattice supersymmetry which are devided into two different cases according to using difference operators. $U(1)_R$ symmetry on the lattice is also realized as one of exact symmetries. For an application, the extended G-W relation is given for a two-dimensional model with chiral multiplets.

- Mitsuhiro Kato, Makoto Sakamoto, Hiroto So 2013/11 Technical reportFor the purpose of constructing supersymmetric(SUSY) theories on lattice, we

propose a new type relation on lattice -cyclic Leibniz rule(CLR)- which is

slightly different from an ordinary Leibniz rule. Actually, we find that CLR

can enlarge the number of SUSYs and construct more Nicolai mappings in a

quantum-mechanical model. In this model, the exact mass degeneracy between

fermion and boson is shown. - Hiroto So, Kazunori Takenaga 2013/02 Technical reportWe introduce a 4-dimensional cutoff in the scenario of gauge-Higgs

unification to control the ultraviolet behavior. A one-loop effective potential

for a Higgs field and the Higgs mass are obtained with the cutoff. We find an

{\it interrelation} between the 4-dimensional cutoff and the scale of extra

dimensions, which is concretized through the Higgs mass. Combining this

interrelation and the recently discovered Higgs boson at LHC, we obtain an

interesting constraint for the 4-dimensional cutoff and the extra dimensional

scale. - Mitsuhiro Kato, Makoto Sakamoto, Hiroto So 2012/12 Technical reportIn a finite volume system, we prove a no-go theorem on a Leibniz rule with a

care of locality argument on latttice. The new possibility on the Leibniz rule

solutions on lattice is discussed. Although the new solution admits a local

difference operator, a non-local product rule is needed. In the case, a

supersymmetric interacting theory is simply realized. The difference between

finite flavor systems and matrix representations of infinite flavor systems is

explained based on a finite volume system analysis including the no-go theorem. - Michika Murata, Hiroto So, Kazunori Takenaga 2010/12 Technical reportIn an SU(2) lattice gauge theory with a Z2 orbifolded extra dimension, the

new symmetry which is called as a stick symmetry is useful in understanding the

bulk transition. We discuss the relation with the Fradkin-Shenker's phase

diagram as well. A remnant of the extra dimension is remained as two U(1) gauge

symmetries in two 4-dimensional spaces. We also consider more general bulk

gauge groups beyond SU(2). - Michika Murata, Hiroto So 2003/06 Technical reportA five-dimensional lattice space can be decomposed into a number of

four-dimens ional lattices called as layers. The five-dimensional gauge theory

on the lattice can be interpreted as four-dimensional gauge theories on the

multi-layer with interactions between neighboring layers. In the theory, there

exist two independent coupling constants; $\beta_4$ controls the dynamics

inside a layer and $\beta_5$ does the strength of the inter-layer

interaction.We propose the new possibility to realize the continuum limit of a

five-dimensional theory using four-dimensional dynamics with large $\beta_4$

and small $\beta_5$. Our result is also related to the higher dimensional

theory by deconstruction approach. - Katsumi Itoh, Mitsuhiro Kato, Hideyuki Sawanaka, Hiroto So, Naoya Ukita Progress of Theoretical Physics 108- (2) 363 -374 2002/08 Technical reportWe present an entirely new approach toward a realization of supersymmetric Yang-Mills theory on the lattice. The action consists of the staggered fermion and the plaquette variables distributed in the Euclidean space with a particular pattern. The system is shown to have fermionic symmetries relating the fermion and link variables.
- Yuji Igarashi, Katsumi Itoh, Hiroto So Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 526- (1-2) 164 -172 2002/01 Technical reportWe present a method to solve the master equation for the Wilsonian action in the antifield formalism. This is based on a representation theory for cutoff-dependent global symmetries along the Wilsonian renormalization group (RG) flow. For the chiral symmetry, the master equation for the free theory yields a continuum version of the Ginsparg-Wilson relation. We construct chiral invariant operators describing fermionic self-interactions. The use of canonically transformed variables is shown to simplify the underlying algebraic structure of the symmetry. We also give another non-trivial example, a realization of SU(2) vector symmetry. Our formalism may be used for a non-perturbative truncation of the Wilsonian action preserving global symmetries. © 2002 Elsevier Science B.V. All rights reserved.
- Yuji Igarashi, Katsumi Itoh, Hiroto So JHEP 0110:032,2001 2001/09 Technical reportUsing the Pauli-Villars regularization, we make a perturbative analysis of

the quantum master equation (QME), $\Sigma =0$, for the Wilsonian effective

action. It is found that the QME for the UV action determines whether exact

gauge symmetry is realized along the renormalization group (RG) flow. The basic

task of solving the QME can be reduced to compute the Troost-van

Niuwenhuizen-Van Proyen jacobian factor for the classical UV action. When the

QME cannot be satisfied, the non-vanishing $\Sigma$ is proportional to a BRS

anomaly, which is shown to be preserved along the RG flow. To see how the UV

action fulfills the QME in anomaly free theory, we calculate the jacobian

factor for a pure Yang-Mills theory in four dimensions. - Yuji Igarashi, Katsumi Itoh, Hiroto So Progress of Theoretical Physics 106- (1) 149 -166 2001/07 Technical reportRecently we made a proposal for realization of an effective BRS symmetry along the Wilsonian renormalization group flow. In this paper we show that the idea can be naturally extended to the most general gauge theories. Extensive use of the antifield formalism is made to reveal some remarkable structure of the effective BRS symmetry. The average action, defined with a continuum analog of the block spin transformation, obeys the quantum master equation (QME), provided that a UV action does so. We show that the RG flow described by the exact flow equations is generated by canonical transformations in the field-antifield space. Using the relation between the average action and the Legendre effective action, we establish the equivalence between the QME for the average action and the modified Ward-Takahashi identity for the Legendre action. The QME remains intact when the regularization is removed.
- Hiroto So, Naoya Ukita Nuclear Physics B - Proceedings Supplements 94- (1-3) 795 -798 2001/03 Technical reportThe Ginsparg-Wilson (G-W) relation for chiral symmetry is extended for a supersymmetrical(SUSY) case on a lattice. It is possible to define exact lattice supersymmetry which are devided into two different cases according to using difference operators. U(1)R symmetry on the lattice is also realized as one of exact symmetries. For an application, the extended G-W relation is given for a two-dimensional model with chiral multiplets. © 2001 Elsevier Science B.V. All rights reserved.
- Minoru Koseki, Hiroto So, Naoya Ukita 2000/11 Technical reportA Ginsparg-Wilson Relation (GWR) is obtained in the presence of chiral

symmetry breaking terms. It leads to the PCAC relation as well as an anomaly

relation on the lattice. For general fermions, the deviation from the exact GWR

is getting small when the block-spin transformations are performed iteratively.

Based on a simple geometrical interpretation of the Dirac operator satisfying

the GWR, we find some physical properties shared by the lattice fermions near

the continuum limit. In two-dimensions, we explicitly construct the GW Dirac

operator by using a conformal mapping. - Yuji Igarashi, Katsumi Itoh, Hiroto So Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 479- (1-3) 336 -342 2000/04 Technical reportWe show that symmetries are preserved exactly along the (Wilsonian) renormalization group flow, though the IR cutoff deforms concrete forms of the transformations. For a gauge theory the cutoff dependent Ward-Takahashi identity is written as the master equation in the antifield formalism: one may read off the renormalized BRS transformation from the master equation. The Maxwell theory is studied explicitly to see how it works. The renormalized BRS transformation becomes non-Local but keeps off-Shell nilpotency. Our formalism is applicable for a generic global symmetry. The master equation considered for the chiral symmetry provides us with the continuum analog of the Ginsparg-Wilson relation and the Luscher'S symmetry. (C) 2000 Elsevier Science B.V.
- Hiroto So, Naoya Ukita Phys.Lett. B457 (1999) 314-318 1998/12 Technical reportThe Ginsparg-Wilson(G-W) relation is extended for supersymmetric free

theories on a lattice.

Exact lattice supersymmetry(SUSY) can be defined without any ambiguities in

difference operators. The lattice action constructed by a block-spin

transformation is invariant under the symmetry. $U(1)_R$ symmetry on the

lattice is also realized as one of exact symmetries.

For an application, the extended G-W relation is given for a two-dimensional

model with chiral-multiplets. It is argued that the relation may be generalized

for interacting cases. - Hiroyuki Kanada, Hiroto So, Shin Takeda 1996/10 Technical reportA Higgs-Yukawa system in a broken phase and Euclidean solutions are

investigated. Although it has been believed that there are no Euclidean

solutions in the broken phase in 4-dimension, we find numerically ones in the

phase due to the effect of a strong Yukawa coupling. The complex Yukawa

coupling is necessary for the stability of the solution. The extension to a

complex Higgs-Yukawa system is also investigated.

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