Holographic Gravitational Anomaly in First and Second Order Hydrodynamics

TL;DR

This paper investigates how chiral and gauge-gravitational anomalies influence relativistic fluid transport properties using holographic models, revealing new second-order effects and corrections to known phenomena.

Contribution

It provides the first detailed second-order holographic computation of anomalous transport coefficients including mixed gauge-gravitational effects.

Findings

Reproduces first-order anomaly-induced currents for magnetic fields and vortices.

Calculates second-order anomalous and non-anomalous transport coefficients.

Discovers a new mixed gauge-gravitational anomaly contribution to shear wave dispersion.

Abstract

We compute, in the framework of the fluid/gravity correspondence, the transport coefficients of a relativistic fluid affected by chiral and gauge-gravitational anomalies, including external electromagnetic fields. The computation is performed at first and second order in the hydrodynamical expansion. We use a 5-dim holographic model with pure gauge and mixed gauge-gravitational Chern-Simons terms in the action. We reproduce at first order previous results on the anomaly induced current of a magnetic field and a vortex in a relativistic fluid, and compute at second order the anomalous and non anomalous transport coefficients by using a Weyl covariant formalism. We find a dissipative and anomalous correction to the chiral magnetic conductivity due to the time dependence of the magnetic field. We also find a new contribution from the mixed gauge-gravitational anomaly to the shear waves dispersion relation. The role played by the chiral and gravitational anomalies in other transport coefficients is discussed.