S-duality in AdS/CFT magnetohydrodynamics

TL;DR

This paper explores how S-duality constrains the hydrodynamics of a charged conformal fluid with an AdS gravity dual, revealing new transport coefficients and surprising vanishing of some at linear order.

Contribution

It derives restrictions on transport coefficients imposed by S-duality and identifies previously undetermined coefficients in holographic conformal fluids.

Findings

Half of the allowed transport coefficients vanish at linear order.

Derived new constraints on fluid transport coefficients from S-duality.

Connected long wavelength perturbations of AdS black branes to boundary fluid dynamics.

Abstract

We study the nonlinear hydrodynamics of a 2+1 dimensional charged conformal fluid subject to slowly varying external electric and magnetic fields. Following recent work on deriving nonlinear hydrodynamics from gravity, we demonstrate how long wavelength perturbations of the AdS dyonic black brane solution of 4D supergravity are governed by equations equivalent to fluid dynamics equations in the boundary theory. We investigate the implications of $S$-duality for our system, and derive restrictions imposed on the transport coefficients of a generic fluid invariant under the S operation. We also expand on our earlier work and determine a new set of previously undetermined transport coefficients for the conformal fluid with an AdS gravity dual. Quite surprisingly, we discover that half of the transport coefficients allowed by symmetry vanish in the holographic fluid at linear order in the hydrodynamic expansion.