Vector-axial vector correlators in weak electric field and the holographic dynamics of the chiral condensate

TL;DR

This paper investigates the behavior of vector-axial vector correlators under weak electric fields using holography, revealing agreement with certain models at low momenta and non-perturbative effects at high momenta.

Contribution

It introduces a holographic model incorporating non-linear chiral condensate dynamics to study correlators in external electric fields, comparing results with existing models.

Findings

Agreement with Son and Yamamoto's relation at low momenta

Divergence of results at large Euclidean momenta

Non-perturbative contributions decrease as q^{-6} at high momenta

Abstract

The transverse part of the vector-axial vector flavor current correlator in the presence of weak external electric field is studied using holography. The correlator is calculated using a bottom-up model arxiv:1003.2377 {proposed recently}, that includes the non-linear dynamics of the chiral condensate. It is shown that for low momenta the result agrees with the relation proposed by arXiv:1010.0718 {Son and Yamamoto} motivated by a simpler holographic model. For large Euclidean momenta however, the two results diverge. In the process, the difference of the vector and axial vector two point functions is also calculated. At large Euclidean momenta it is found that the first non-perturbative contribution, decreases as $q^{-6}$ as expected from QCD.