arXiv subjects

Hiroto So

Publications and source records attributed to Hiroto So.

31 records · Page 2Linked to original sources

arXiv2003

Five-dimensional Lattice Gauge Theory as Multi-Layer World

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; $β_4$ controls the dynamics inside a layer and $β_5$ 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 $β_4$ and small $β_5$. Our result is also related to the higher dimensional theory by deconstruction approach.

hep-lat↗

arXiv2002

Lattice Chiral Symmetry in Fermionic Interacting Theories and the Antifield Formalism

Recently 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.

hep-lat↗

arXiv2002

Ginsparg-Wilson Relation and Lattice Chiral Symmetry in Fermionic Interacting Theories

We 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.

hep-lat↗

arXiv2001

Towards the Super Yang-Mills Theory on the Lattice

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.

hep-lat↗

arXiv2001

Realization of Global Symmetries in the Wilsonian Renormalization Group

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.

hep-th↗

arXiv2001

Regularized Quantum Master Equation in the Wilsonian Renormalization Group

Using the Pauli-Villars regularization, we make a perturbative analysis of the quantum master equation (QME), $Σ=0$, 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 $Σ$ 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.

hep-th↗

arXiv2001

BRS Symmetry, the Quantum Master Equation, and the Wilsonian Renormalization Group

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.

hep-th↗

arXiv2000

What happens to Lattice Fermion near Continuum Limit?

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.

hep-lat↗

arXiv2000

Exact BRS Symmetry realized on the Renormalization Group Flow

Using the average action defined with a continuum analog of the block spin transformation, we show the presence of gauge symmetry along the Wilsonian renormalization group flow. As a reflection of the gauge symmetry, the average action satisfies the quantum master equation(QME). We show that the quantum part of the master equation is 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.

hep-th↗

arXiv2000

Exact Symmetries realized on the Renormalized Group Flow

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{\" u}scher's symmetry.

hep-th↗

arXiv1999

Ginsparg-Wilson Relation and Lattice Supersymmetry

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.

hep-lat↗

arXiv1996

Euclidean Solutions in Broken Phase and Electro-Weak Dynamics

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.

hep-ph↗

arXiv1995

Baryon and Lepton Number Assignment in $E_6$ Models

In $E_6$ 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 left-right symmetric extension of the standard model in which $(B-L)$ 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, {\it i.e.}, there is no non-perturbative baryon or lepton number violation during the electroweak phase transition. We study some consequences of the new assignment.

hep-ph↗