arXiv subjects

Yuji Igarashi

Publications and source records attributed to Yuji Igarashi.

At least 19 recordsLinked to original sources

arXiv2025

Functional Renormalization Group Flows and Gauge Consistency in QED

We consider quantum electrodynamics with chiral four-Fermi interactions in the functional renormalization group approach. In gauge theories, the functional flow equation for the effective action is accompanied by the quantum master equation that governs the underlying gauge symmetry. Beyond perturbation theory, fully gauge-consistent solutions are very difficult to obtain. We devise a systematic expansion scheme in which the solutions of the flow equation also solve the Quantum Master Equation. In the present work we apply this construction within the lowest order corrections in the photon two-point functions. In this truncation we discuss the phase structure in terms of the gauge and four-Fermi couplings based on a numerical solution of the system.

hep-th↗

arXiv2025

Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction

We theoretically investigate three-dimensional singular flat band systems, focusing on their quantum geometric properties and response to external magnetic fields. As a representative example, we study the pyrochlore lattice, which hosts a pair of degenerate flat bands touching a dispersive band. We derive a three-orbital effective continuum model that captures the essential features near the band-touching point. Within this framework, we identify the point-like topological singularity on a planar manifold defined by the degenerate flat band eigenvectors. This singularity strongly influences the quantum geometry and results in a characteristic Landau level structure, where the levels spread over a finite energy range. We show that this structure reflects the underlying band reconstruction due to the orbital Zeeman effect, which lifts the flat band degeneracy and induces the Weyl-semimetal-like dispersion near the singularity. Our analysis reveals that the range of Landau level spreading is proportional to the quantum metric of each Zeeman-split band. We further demonstrate that adding a small dispersion via longer-range . Finally, we show that our approach extends naturally to systems with higher orbital angular momentum, indicating the robustness of these features in a broad class of three-dimensional flat band models.

cond-mat.mes-hall↗

arXiv2021

QED in the Exact Renormalization Group

The functional flow equation and the Quantum Master equation are consistently solved in perturbation for the chiral symmetric QED with and without four-fermi interactions. Due to the presence of momentum cutoff, unconventional features related to gauge symmetry are observed even in our perturbative results. In the absence of the four-fermi couplings, one-loop calculation gives us the Ward identity, $Z_{1}=Z_{2}$, and the standard results of anomalous dimensions and the beta function for the gauge coupling. It is a consequence of regularization scheme independence in one-loop computation. We also find a photon mass term. When included, four-fermi couplings contribute to the beta function and the Ward identity is also modified, $Z_{1} \neq Z_{2}$, due to a term proportional to the photon mass multiplied by the four-fermi couplings.

hep-th↗

arXiv2019

BRST in the Exact RG

We show that the Quantum Master Equation and the Wilsonian renormalization group (RG) flow equation can be combined such that for the continuum effective action, quantum BRST invariance is not broken by the presence of an effective ultraviolet cutoff $Λ$, despite the fact that the structure demands quantum corrections that naively break the gauge invariance, such as a mass term for a non-Abelian gauge field. Exploiting the derivative expansion, BRST cohomological methods fix the solution up to choice of renormalization conditions, without inputting the form of the classical, or bare, interactions. Legendre transformation results in an equivalent description in terms of solving the modified Slavnov-Taylor identities and the flow of the Legendre effective action under an infrared cutoff $Λ$ (i.e. effective average action). The flow generates a canonical transformation that automatically solves the Slavnov-Taylor identities for the wavefunction renormalization constants. We confirm this structure in detail at tree level and one loop. Under flow of $Λ$, the standard results are obtained for the beta function, anomalous dimension, and physical amplitudes, up to choice of renormalization scheme.

hep-th↗

arXiv2016

Functional flows in QED and the modified Ward-Takahashi identity

In the functional renormalisation group approach to gauge theory, the Ward-Takahashi identity is modified due to the presence of an infrared cutoff term. It take the most accessible form for the Wilsonian effective action. In the present work we solve these identities, partially, for the Wilson effective action of QED. In particular, we compute the longitudinal part of the photon two point vertex function as a momentum- dependent function in the presence of the cutoff k. The resultant Wilsonian effective action carries form factors that originate from the modified Ward-Takahashi identity. We show how this result carries over to the one-particle-irreducible effective action.

hep-th↗

arXiv2013

Blocking-inspired supersymmetric actions: a status report

We provide a status report on the advances in blocking-inspired supersymmetric actions. This is done at the example of interacting supersymmetric quantum mechanics as well as the Wess-Zumino model. We investigate in particular the implications of a nontrivial realisation of translational symmetry on the lattice in this approach. We also discuss the locality of symmetry generators.

hep-lat↗

arXiv2011

Realization of Chiral Symmetry in the ERG

We discuss within the framework of the ERG how chiral symmetry is realized in a linear $σ$ model. A generalized Ginsparg-Wilson relation is obtained from the Ward-Takahashi identities for the Wilson action assumed to be bilinear in the Dirac fields. We construct a family of its non-perturbative solutions. The family generates the most general solutions to the Ward-Takahashi identities. Some special solutions are discussed. For each solution in this family, chiral symmetry is realized in such a way that a change in the Wilson action under non-linear symmetry transformation is canceled with a change in the functional measure. We discuss that the family of solutions reduces via a field redefinition to a family of the Wilson actions with some composite object of the scalar fields which has a simple transformation property. For this family, chiral symmetry is linearly realized with a continuum analog of the operator extension of $γ_5$ used on the lattice. We also show that there exist some appropriate Dirac fields which obey the standard chiral transformations with $γ_5$ in contrast to the lattice case. Their Yukawa interactions with scalars, however, becomes non-linear.

hep-th↗

arXiv2011

Anomalies in the ERG Approach

The antifield formalism adapted in the exact renormalization group is found to be useful for describing a system with some symmetry, especially the gauge symmetry. In the formalism, the vanishing of the quantum master operator implies the presence of a symmetry. The QM operator satisfies a simple algebraic relation that will be shown to be related to the Wess-Zumino condition for anomalies. We also explain how an anomaly contributes to the QM operator.

hep-th↗

arXiv2009

CP invariance of chiral gauge theories and Majorana-Yukawa couplings on the lattice

The construction of CP-invariant lattice chiral gauge theories and the construction of lattice Majorana fermions with chiral Yukawa couplings is subject to topological obstructions. In the present work we suggest lattice extensions of charge and parity transformation for Weyl fermions. This enables us to construct lattice chiral gauge theories that are CP invariant. For the construction of Majorana-Yukawa couplings, we discuss two models with symplectic Majorana fermions: a model with two symplectic doublets, and one with an auxiliary doublet.

hep-lat↗

arXiv2009

Realization of symmetry in the ERG approach to quantum field theory

We review the use of the exact renormalization group for realization of symmetry in renormalizable field theories. The review consists of three parts. In part I (sects. 2,3,4), we start with the perturbative construction of a renormalizable field theory as a solution of the exact renormalization group (ERG) differential equation. We show how to characterize renormalizability by an appropriate asymptotic behavior of the solution for a large momentum cutoff. Renormalized parameters are introduced to control the asymptotic behavior. In part II (sects. 5--9), we introduce two formalisms to incorporate symmetry: one by imposing the Ward-Takahashi identity, and another by imposing the generalized Ward-Takahashi identity via sources that generate symmetry transformations. We apply the two formalisms to concrete models such as QED, YM theories, and the Wess-Zumino model in four dimensions, and the O(N) non-linear sigma model in two dimensions. We end this part with calculations of the abelian axial and chiral anomalies. In part III (sects. 10,11), we overview the Batalin-Vilkovisky formalism adapted to the Wilson action of a bare theory with a UV cutoff. We provide a few appendices to give details and extensions that can be omitted for the understanding of the main text. The last appendix is a quick summary for the reader's convenience.

hep-th↗

arXiv2009

Majorana fermions and CP-invariance of chiral gauge theories on the lattice

The construction of massless Majorana fermions with chiral Yukawa couplings on the lattice is considered. We find topological obstructions tightly linked to those underlying the Nielsen-Ninomiya no-go theorem. In contradistinction to chiral fermions the obstructions originate only from the combination of the Dirac action and the Yukawa term. These findings are used to construct a chirally invariant lattice action. We also show that the path integral of this theory is given by the Pfaffian of the corresponding Dirac operator. As an application of the approach set-up here we construct a CP-invariant lattice action of a chiral gauge theory, based on a lattice adaptation of charge conjugation and parity transformation in the continuum.

hep-lat↗

arXiv2008

Ward-Takahashi identity for Yang-Mills theory in the Exact Renormalization Group

We give a functional derivation of the Ward-Takahashi identity for Yang-Mills theory in the framework of the exact renormalization group. The identity realizes non-abelian gauge symmetry nontrivially despite the presence of a momentum cutoff. The cutoff deforms the gauge transformation by introducing composite operators. In our functional method, which is an extension of the method used in our previous work on QED, these composite operators are expressed in terms of the Wilson action that depends on both a UV cutoff and an IR cutoff.

hep-th↗

arXiv2007

On Majorana fermions on the lattice

The construction of massless Majorana fermions with chiral Yukawa couplings on the lattice is considered. We find topological obstructions tightly linked to those underlying the Nielsen-Ninomiya no-go theorem. In contradistinction to chiral fermions the obstructions originate only from the combination of the Dirac action and the Yukawa term. These findings are used to construct a chirally invariant lattice action. We also show that the path intgral of this theory is given by the Pfaffian of the corresponding Dirac operator.

hep-lat↗

arXiv2007

Quantum Master Equation for QED in Exact Renormalization Group

Recently, one of us (H.S.) gave an explicit form of the Ward-Takahashi identity for the Wilson action of QED. We first rederive the identity using a functional method. The identity makes it possible to realize the gauge symmetry even in the presence of a momentum cutoff. In the cutoff dependent realization, the abelian nature of the gauge symmetry is lost, breaking the nilpotency of the BRS transformation. Using the Batalin-Vilkovisky formalism, we extend the Wilson action by including the antifield contributions. Then, the Ward-Takahashi identity for the Wilson action is lifted to a quantum master equation, and the modified BRS transformation regains nilpotency. We also obtain a flow equation for the extended Wilson action.

hep-th↗

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

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↗