Axial anomalies in gauge theory by exact renormalization group method

TL;DR

This paper investigates axial anomalies in an $SU(2)$ gauge theory using an exact renormalization group approach, focusing on boundary conditions at the physical scale rather than the ultraviolet limit.

Contribution

It introduces a novel RG framework that implements chiral symmetry through boundary conditions at the physical scale, enabling direct computation of axial anomalies.

Findings

Successfully computes triangle axial anomalies within the RG framework

Demonstrates the implementation of chiral symmetry via boundary conditions at $ ext{L}=0$

Provides a new perspective on gauge theories using exact RG methods

Abstract

The global chiral symmetry of a $SU(2)$ gauge theory is studied in the framework of renormalization group (RG). The theory is defined by the RG flow equations in the infrared cutoff $\L$ and the boundary conditions for the relevant couplings. The physical theory is obtained at $\L=0$. In our approach the symmetry is implemented by choosing the boundary conditions for the relevant couplings not at the ultraviolet point $\L=\L_0\to\infty$ but at the physical value $\L=0$. As an illustration, we compute the triangle axial anomalies.