arXiv subjects

Hidenori Sonoda

Publications and source records attributed to Hidenori Sonoda.

At least 19 recordsLinked to original sources

arXiv2026

Explicit construction of the energy-momentum tensor in the large N limit of a four-Fermi theory

Using the exact renormalization group (functional RG) formalism, we construct the energy-momentum tensor of a four-Fermi theory in the Euclidean space of dimensions 2 < D < 4 in the large N limit, where N is the number of Dirac fields. The energy-momentum tensor is a functional of the Dirac fields, and its cutoff dependence is controlled by the exact RG equation. In the zero cutoff limit the functional reduces to the one-particle-irreducible effective action with a single insertion of the energy-momentum tensor. At a finite cutoff the energy-momentum tensor satisfies the Ward-Takahashi identity for translation invariance, and its antisymmetric part is determined by rotation invariance. We also show that the critical theory is conformally invariant by deriving the corresponding Ward-Takahashi identity.

hep-th↗

arXiv2026

Explicit construction of the energy-momentum tensor in the large N limit

We construct the energy-momentum tensor of the O(N) linear sigma model explicitly in the large N limit using the exact renormalization group (ERG) formalism. The energy-momentum tensor is obtained as a cutoff dependent functional of N scalar field variables. Our guiding principles behind the construction are twofold: first the energy-momentum tensor must satisfy the Ward identity for translation and rotation invariance, and second the energy-momentum tensor must satisfy a variant of the exact renormalization group equation. In the limit that the momentum cutoff goes to zero, our energy-momentum tensor gives the one-particle irreducible (1PI) effective action with the insertion of a single energy-momentum tensor operator. We verify that the energy-momentum tensor constructed satisfies the expected trace formula, and that the trace vanishes at the Wilson-Fisher critical point.

hep-th↗

arXiv2025

A basis of the gradient flow exact renormalization group for gauge theory

The gradient flow exact renormalization group (GFERG) is a variant of the exact renormalization group (ERG) for gauge theory that is aimed at preserve gauge invariance as manifestly as possible. It achieves this goal by utilizing the Yang--Mills gradient flow or diffusion for the block-spin process. In this paper, we formulate GFERG by the Reuter equation in which the block spinning is done by Gaussian integration. This formulation provides a simple understanding of various points of GFERG, unresolved thus far. First, there exists a unique ordering of functional derivatives in the GFERG equation that remove ambiguity of contact terms. Second, perturbation theory of GFERG suffers from unconventional ultraviolet (UV) divergences if no gauge fixing is introduced. This explains the origin of some UV divergences we have encountered in perturbative solutions to GFERG. Third, the modified correlation functions calculated with the Wilson action in GFERG coincide with the correlation functions of diffused or flowed fields calculated with the bare action. This shows the existence of a Wilson action that reproduces precisely the physical quantities computed by the gradient flow formalism (up to contact terms). We obtain a definite ERG interpretation of the gradient flow. The formulation given in this paper provides a basis for further perturbative/nonperturbative computations in GFERG, preserving gauge invariance maximally.

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arXiv2024

Background dependent cutoff for Wilson actions

We study the application of the background field method in the framework of the exact renormalization group (ERG). By considering the case of a scalar field theory, we provide a detailed discussion of the properties satisfied by a background dependent Wilson action. We show how the Ward identity associated with background field shifts for the Wilson action is related to that for the 1PI Wilson action, or effective average action. Moreover, we discuss the ERG equations in the dimensionless framework and emphasize the role of the Ward identity in this setting. We give two examples: the Gaussian fixed point for the real scalar theory and the large $N$ limit of the linear sigma model.

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arXiv2024

On the field independent additive constant in Wilson actions

We discuss the field independent additive constant in Wilson actions carefully within the exact renormalization group formalism. The additive constant does not affect the correlation functions of fields normalized by the partition function, and for that reason it is often ignored. But it is an essential part of the partition function, and in the limit where the UV cutoff goes to zero, the constant gives a renormalized vacuum energy density. We discuss two concrete examples: the Gaussian theory and the linear sigma model in the large $N$ limit.

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arXiv2024

Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism

The gradient flow exact renormalization group (GFERG) is an idea that incorporates gauge invariant gradient flows into the formalism of the exact renormalization group (ERG). GFERG introduces a Wilson action with a cutoff while keeping vector gauge invariance manifestly. The details of the formalism are still to be worked out. In this paper, we apply GFERG to construct the Wilson action of massless Dirac fermions under the background chiral gauge fields. By formulating the chiral anomaly as a ``composite operator,'' we make the scale invariance of the anomaly manifest. We argue that the same result extends to QCD.

hep-th↗

arXiv2023

Exact Renormalization Group in Large $N$

We apply the exact renormalization group formalism to compute the effective action and potential of the four dimensional O$(N)$ linear sigma model in large $N$. With a finite momentum cutoff in place, the model is well defined. In the naive continuum limit where the cutoff is taken to infinity, the effective action suffers from a tachyon, and the effective potential is unbounded from below and develops a negative imaginary part. These problems disappear once a small enough cutoff is restored. The effective potential of the naive continuum limit, obtained by analytic continuation, is given explicitly in terms of the Lambert $W$ function.

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arXiv2022

Renormalization for a model of photon scattering off a charged harmonic oscillator

In the electric dipole approximation the model of a charged harmonic oscillator interacting with the radiation field becomes quadratic and soluble, but it needs a UV cutoff for the photon frequency. The model's renormalizability is only apparent; physics requires that the cutoff be kept finite. The cutoff plays the role of a parameter that characterizes the high frequency behavior of the photon cross section.

quant-ph↗

arXiv2022

One-particle irreducible Wilson action in the gradient flow exact renormalization group formalism

We define a one-particle irreducible (1PI) Wilson action in the gradient flow exact renormalization group (GFERG) formalism as the Legendre transform of a Wilson action. We consider quantum electrodynamics in particular, and show that the GFERG flow equation preserves the invariance of the 1PI Wilson action (excluding the gauge-fixing term) under the \emph{conventional\/} $U(1)$ gauge transformation. This is in contrast to the invariance of the original Wilson action under a modified $U(1)$ gauge transformation. The global chiral transformation also takes the \emph{conventional\/} form for the 1PI Wilson action. Despite the complexity of the GFERG flow equation, the conventional form of the gauge and global chiral transformations may allow us to introduce a non-perturbative Ansatz for gauge and chiral invariant 1PI Wilson actions.

hep-th↗

arXiv2021

Manifestly gauge invariant exact renormalization group for quantum electrodynamics

We formulate quantum electrodynamics on the basis of gauge (or BRST) covariant diffusion equations of fields. This is a particular example of the gradient flow exact renormalization group (GFERG). The resulting Wilson action fulfills a simple gauge Ward--Takahashi identity. We solve the GFERG equation around the Gaussian fixed point to the second order in gauge coupling and obtain the 1-loop beta function and anomalous dimensions. The anomalous dimension of the electron field coincides with that of the fermion field diffused by a gauge covariant flow equation of Lüscher.

hep-th↗

arXiv2021

Gradient flow exact renormalization group

The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of the Wilson action in the exact renormalization group (ERG) formalism. By imitating the structure of this connection, we propose an ERG differential equation that preserves manifest gauge invariance in Yang--Mills theory. Our construction in continuum theory can be extended to lattice gauge theory.

hep-th↗

arXiv2019

Derivation of a Gradient Flow from ERG

We establish a concrete correspondence between a gradient flow and the renormalization group flow for a generic scalar field theory. We use the exact renormalization group formalism with a particular choice of the cutoff function.

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arXiv2018

Conformal invariance for Wilson actions

We discuss the realization of conformal invariance for Wilson actions using the formalism of the exact renormalization group. This subject has been studied extensively in the recent works of O. J. Rosten. The main purpose of this paper is to reformulate Rosten's formulas for conformal transformations using a method developed earlier for the realization of any continuous symmetry in the exact renormalization group formalism. The merit of the reformulation is simplicity and transparency via the consistent use of equation-of-motion operators. We derive equations that imply the invariance of the Wilson action under infinitesimal conformal transformations which are non-linearly realized but form a closed conformal algebra. The best effort has been made to make the paper self-contained; ample background on the formalism is provided.

hep-th↗

arXiv2017

A Holographic form for Wilson's RG

An attempt is made to make precise the connection between Wilson's RG and "Holographic RG" by writing Wilson's RG in a holographic form. A functional formulation is given for the exact RG evolution of a scalar field in $d$ (flat) dimensions. It is shown that a change of variables maps the action to that for a scalar field in $AdS_{d+1}$. This provides a holographic form for Wilson's RG that can be called "Holographic RG". This mapping can only be done for a specific form of the cutoff function in the Exact Renormalization Group formalism. The notion of scale and conformal invariance in the presence of a {\em finite} UV cutoff is emphasized. The discussion is primarily about the two-point function and the Gaussian fixed point. Some remarks are made about nontrivial fixed points.

hep-th↗

arXiv2013

Gauge invariant composite operators of QED in the exact renormalization group formalism

Using the exact renormalization group (ERG) formalism, we study the gauge invariant composite operators in QED. Gauge invariant composite operators are introduced as infinitesimal changes of the gauge invariant Wilson action. We examine the dependence on the gauge fixing parameter of both the Wilson action and gauge invariant composite operators. After defining ``gauge fixing parameter independence,'' we show that any gauge independent composite operators can be made ``gauge fixing parameter independent'' by appropriate normalization. As an application, we give a concise but careful proof of the Adler-Bardeen non-renormalization theorem for the axial anomaly in an arbitrary covariant gauge by extending the original proof by A. Zee.

hep-th↗

arXiv2013

Analytic form of the effective potential in the large N limit of a real scalar theory in four dimensions

We give the large N limit of the effective potential for the O(N) linear sigma model in four dimensions in terms of the Lambert W function. The effective potential is fully consistent with the renormalization group, and it admits an asymptotic expansion in powers of a small positive coupling parameter. Careful consideration of the UV cutoff present in the model validates the physics of the large N limit.

hep-th↗

arXiv2011

Phase structure of a three-dimensional Yukawa model

We use the method of the exact renormalization group to study the renormalization group flows of an O(N) invariant Yukawa model in three dimensional Euclidean space consisting of one real scalar and N real spinor fields. We obtain a phase structure similar to that of the N-vector model with cubic anisotropy, possessing a region of parameters exhibiting a first order transition. The particular case with one real fermion (N=1) belongs to the same universality class as the Wess-Zumino model with one supersymmetry. For the critical exponents of the Wilson-Fisher type fixed points, our 1-loop approximations are generally consistent with the results of previous studies.

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.

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