研究者データベース

宗 博人ソウ ヒロト

所属部署名大学院理工学研究科 数理物質科学専攻
職名教授
Last Updated :2019/10/08

研究者基本情報

基本情報

氏名

  • 氏名

    宗 博人
  • 氏名(カナ)

    ソウ ヒロト

学歴等

学位

  • 理学博士

研究活動情報

研究分野等

研究分野

  • 物理学, 素粒子・原子核・宇宙線・宇宙物理

研究キーワード

  • 超対称性
  • 格子場の理論
  • 統一理論
  • 素粒子論

著書・発表論文等

論文

講演・口頭発表等

  • 符号問題とCLR(巡回ライプニッツ則), 宗 博人, 京大基研地域スクール:四国セミナー2018, 2018年12月
  • Numerical analysis of supersymmetric quantum mechanics on lattice with cyclic Leibniz rule, 加堂 大輔、亀井 武成、宗 博人, 日本物理学会2018年秋季大会, 2018年09月
  • Cohomological property of CLR-realized supersymmetric quantum mechanics on lattice, 加藤光裕、坂本眞人、宗博人, 日本物理学会第71回年次大会(2016年), 2016年03月
  • Non-renormalization theorem and cyclic Leibniz rule in lattice supersymmetry, Mitsuhiro Kato, Makoto Sakamoto, Hiroto So, Proceedings of Science, 2014年01月, © 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.
  • Cyclic Leibniz rule: A formulation of supersymmetry on lattice, Mitsuhiro Kato, Makoto Sakamoto, Hiroto So, Proceedings of Science, 2013年01月, © 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, Mitsuhiro Kato, Makoto Sakamoto, Hiroto So, Proceedings of Science, 2012年01月, In 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.
  • 5-dimensional SU(2) lattice gauge theory with Z<inf>2</inf> orbifolding and its phase structure, Michika Murata, Hiroto So, Kazunori Takenaga, Proceedings of Science, 2010年01月, © 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).
  • No-Go Theorem of Leibniz Rule and Supersymmetry on the Lattice, Mitsuhiro Kato, Makoto Sakamoto, Hiroto So, PoS LATTICE2008:233,2008, 2008年10月, 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.
  • No-go theorem of Leibniz rule and supersymmetry on the lattice, Mitsuhiro Kato, Makoto Sakamoto, Hiroto So, Proceedings of Science, 2008年01月, © 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, Hiroto So, Masashi Hayakawa, Hiroshi Suzuki, PoSLAT2006:047,2006, 2006年10月, On 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, Mitsuhiro Kato, Makoto Sakamoto, Hiroto So, PoS LAT2005 (2005) 274, 2005年09月, We 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, Hiroto. So, Naoya Ukita, Nucl.Phys.Proc.Suppl. 94 (2001) 795-798, 2000年11月, The 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.

MISC

  • Non-renormalization theorem and cyclic Leibniz rule in lattice supersymmetry, Mitsuhiro Kato, Makoto Sakamoto, Hiroto So, 2014年11月, http://arxiv.org/abs/1411.1128v1, 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.
  • Cyclic Leibniz rule: a formulation of supersymmetry on lattice, Mitsuhiro Kato, Makoto Sakamoto, Hiroto So, 2013年11月, http://arxiv.org/abs/1311.4962v2, 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.
  • Is the Higgs a sign of extra dimensions?, Hiroto So, Kazunori Takenaga, 2013年02月, 10.1103/PhysRevD.88.016001, http://arxiv.org/abs/1302.0460v3, We 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.
  • Leibniz rule, locality and supersymmetry on lattice, Mitsuhiro Kato, Makoto Sakamoto, Hiroto So, 2012年12月, http://arxiv.org/abs/1212.1533v1, In 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.
  • 5-dimensional SU(2) lattice gauge theory with Z2 orbifolding and its phase structure, Michika Murata, Hiroto So, Kazunori Takenaga, 2010年12月, http://arxiv.org/abs/1012.2727v1, 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).
  • Five-dimensional Lattice Gauge Theory as Multi-Layer World, Michika Murata, Hiroto So, 2003年06月, http://arxiv.org/abs/hep-lat/0306003v2, A 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.
  • Towards the Super Yang-Mills Theory on the Lattice, Katsumi Itoh, Mitsuhiro Kato, Hideyuki Sawanaka, Hiroto So, Naoya Ukita, Prog.Theor.Phys. 108 (2002) 363-374, 2001年12月, 10.1143/PTP.108.363, http://arxiv.org/abs/hep-lat/0112052v1, We present an entirely new approach towards a realization of the 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 the link variables.
  • Realization of Global Symmetries in the Wilsonian Renormalization Group, Yuji Igarashi, Katsumi Itoh, Hiroto So, Phys.Lett. B526 (2002) 164-172, 2001年11月, 10.1016/S0370-2693(01)01461-7, http://arxiv.org/abs/hep-th/0111112v1, We 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.
  • Regularized Quantum Master Equation in the Wilsonian Renormalization Group, Yuji Igarashi, Katsumi Itoh, Hiroto So, JHEP 0110:032,2001, 2001年09月, 10.1088/1126-6708/2001/10/032, http://arxiv.org/abs/hep-th/0109202v1, Using 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.
  • BRS Symmetry, the Quantum Master Equation, and the Wilsonian Renormalization Group, Yuji Igarashi, Katsumi Itoh, Hiroto So, Prog.Theor.Phys. 106 (2001) 149-166, 2001年01月, 10.1143/PTP.106.149, http://arxiv.org/abs/hep-th/0101101v1, Recently 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 for 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 an 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.
  • What happens to Lattice Fermion near Continuum Limit?, Minoru Koseki, Hiroto So, Naoya Ukita, 2000年11月, http://arxiv.org/abs/hep-lat/0011009v1, A 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.
  • Exact Symmetries realized on the Renormalized Group Flow, Yuji Igarashi, Katsumi Itoh, Hiroto So, Phys.Lett. B479 (2000) 336-342, 1999年12月, 10.1016/S0370-2693(00)00305-1, http://arxiv.org/abs/hep-th/9912262v2, We 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 L{\&quot; u}scher's symmetry.
  • Ginsparg-Wilson Relation and Lattice Supersymmetry, Hiroto So, Naoya Ukita, Phys.Lett. B457 (1999) 314-318, 1998年12月, 10.1016/S0370-2693(99)00539-0, http://arxiv.org/abs/hep-lat/9812002v3, The 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.
  • Euclidean Solutions in Broken Phase and Electro-Weak Dynamics, Hiroyuki Kanada, Hiroto So, Shin Takeda, 1996年10月, http://arxiv.org/abs/hep-ph/9610519v2, A 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.

その他研究情報

競争的資金

愛媛大学教員活動実績

教育活動(B)

論文指導(B07)

  • 2016年, 4, 1, 1, 0, 1, 0, 0, 0

論文審査(B10)

  • 2016年, 1, 1, 0, 0


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