Holographic Non-Abelian Charged Hydrodynamics from the Dynamics of Null Horizons

TL;DR

This paper derives non-abelian charged hydrodynamics from null horizon dynamics in a 5D spacetime, incorporating anomalies and vorticity, with applications to AdS/CFT correspondence and black brane horizons.

Contribution

It establishes a holographic framework linking null hypersurface dynamics to non-abelian hydrodynamics with anomalies, providing explicit transport coefficients and entropy current expressions.

Findings

Hydrodynamics with non-abelian charges derived from horizon dynamics.

Inclusion of Chern-Simons terms leads to anomalous vorticity effects.

Explicit transport coefficients obtained for arbitrary equations of state.

Abstract

We analyze the dynamics of a four-dimensional null hypersurface in a five-dimensional bulk spacetime with Einstein-Yang-Mills fields. In an appropriate ansatz, the projection of the field equations onto the hypersurface takes the form of conservation laws for relativistic hydrodynamics with global non-abelian charges. A Chern-Simons term in the bulk action corresponds to anomalies in the global charges, with a vorticity term arising in the hydrodynamics. We derive the entropy current and obtain unique expressions for some of the leading-order transport coefficients (in the abelian case, all of them) for arbitrary equations of state. As a special case and a concrete example, we discuss the event horizon of a boosted Einstein-Yang-Mills black brane in an asymptotically Anti-de-Sitter spacetime. The evolution equations in that case describe the hydrodynamic limit of a conformal field theory with anomalous global non-abelian charges on the Anti-de-Sitter boundary.