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

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.