Chiral Magnetic Effect and Three-point Function from AdS/CFT Correspondence

TL;DR

This paper calculates the chiral magnetic current in a strongly coupled gauge theory using AdS/CFT, revealing non-local effects of fluctuating chiral imbalance and providing insights relevant to heavy ion collision phenomenology.

Contribution

It introduces a novel calculation of the AVV three-point function response to space-time dependent axial fields in AdS/CFT, extending understanding beyond constant chemical potential treatments.

Findings

Chiral magnetic current depends non-locally on chiral imbalance.

The AVV three-point function is expressed via Heun functions and shown to be UV/IR finite.

Results highlight the non-local nature of chiral magnetic effects in dynamic conditions.

Abstract

The chiral magnetic effect with a fluctuating chiral imbalance is more realistic in the evolution of quark-gluon plasma, which reflects the random gluonic topological transition. Incorporating this dynamics, we calculate the chiral magnetic current in response to space-time dependent axial gauge potential and magnetic field in AdS/CFT correspondence. In contrast to conventional treatment of constant axial chemical potential, the response function here is the AVV three-point function of the $\mathcal{N}=4$ super Yang-Mills at strong coupling. Through an iterative solution of the nonlinear equations of motion in Schwarzschild-AdS$_5$ background, we are able to express the AVV function in terms of two Heun functions and prove its UV/IR finiteness, as expected for $\mathcal{N}=4$ super Yang-Mills theory. We found that the dependence of the chiral magnetic current on a non-constant chiral imbalance is non-local, different from hydrodynamic approximation, and demonstrates the subtlety of the infrared limit discovered in field theoretic approach. We expect our results enrich the understanding of the phenomenology of the chiral magnetic effect in the context of relativistic heavy ion collisions.