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-AdS5 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.
Highlights
Chiral anomaly is reflected in the anomalous Ward identity of the axial-vector current JAμ in the presence of vector and axial vector field strengths (F V)μν and (F A)μν
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
Hydrodynamic simulations have been developed for RHIC, based on the assumption that a net axial charge density is generated in the initial stage of collisions and its characteristic time of variation is much longer than the relaxation time to thermal equilibrium [24,25,26]
Summary
All we need to do is to solve the Maxwell-Chern-Simons equations (2.8) and (2.9) with (V, A) replaced by the fluctuations {A, V} and the metric fixed to the AdS-Schwarzschild background (2.18), i.e. The AdS-boundary conditions V0(xμ; u) u→0 ≡ 0 because of the zero R-charge chemical potential we assumed; V(xμ; u) u→0 = 0 that leads to a spacetime-dependent magnetic field B(xμ); and A0(xμ; u) u→0 = 0 that proxies a spacetime-dependent chiral imbalance in a strongly-coupled quark-gluon plasma. Employing the probe approximation can dismiss the backreaction [20, 21], and work on the AdS-Schwarzschild background, but the condition κM/κEM 1 is artificially required, which renders the boundary field theory not the super Yang-Mills
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