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

Christopher Eling, Yasha Neiman, Yaron Oz

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.

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

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.

Paper Structure

This paper contains 39 sections, 1 theorem, 148 equations.

Table of Contents

  1. Introduction and Summary
  2. The Geometrical Framework
  3. Horizon geometry
  4. Yang-Mills
  5. Field equations
  6. Bulk equations
  7. Horizon equations
  8. The AdS black brane
  9. The homogeneous solution
  10. Thermodynamic quantities
  11. Inhomogeneous solution: outline of the calculation
  12. Ideal hydrodynamics
  13. Charge tensors constructed from $n^a$
  14. Scalars
  15. Vectors
  16. ...and 24 more sections

Key Result

Proposition 4.1

All matrices constructed from $n^a$ with indices in $Z^\bot(\mathbf{n})$ commute with all other matrices constructed from $n^a$

Theorems & Definitions (1)

  • Proposition 4.1