Anomaly matching condition in two-dimensional systems

TL;DR

This paper derives a non-perturbative anomaly matching condition in two-dimensional systems, connecting current correlators and analyzing its validity across energy scales using holographic RG flows.

Contribution

It introduces a two-dimensional analog of the Son-Yamamoto relation and demonstrates its stability across energy scales via holographic RG flow analysis.

Findings

The relation connects transverse and diagonal current correlators in 2D systems.

The Son-Yamamoto relation remains valid over a wide range of energy scales.

Holographic RG flows preserve the relation's form across scales.

Abstract

Based on Son-Yamamoto relation obtained for transverse part of triangle axial anomaly in ${\rm QCD}_4$, we derive its analog in two-dimensional system. It connects the transverse part of mixed vector-axial current two-point function with diagonal vector and axial current two-point functions. Being fully non-perturbative, this relation may be regarded as anomaly matching for conductivities or certain transport coefficients depending on the system. We consider the holographic RG flows in holographic Yang-Mills-Chern-Simons theory via the Hamilton-Jacobi equation with respect to the radial coordinate. Within this holographic model it is found that the RG flows for the following relations are diagonal: Son-Yamamoto relation and the left-right polarization operator. Thus the Son-Yamamoto relation holds at wide range of energy scales.