Bulk Viscosity in Holographic Lifshitz Hydrodynamics

TL;DR

This work computes bulk viscosity in holographic models with Lifshitz scaling and hyperscaling violation, showing that Lifshitz-invariant theories with massive-vector backgrounds have vanishing bulk viscosity, while broader classes with scalars or massless vectors yield a universal $\zeta/\eta$ that depends on the dynamical exponent $z$ and hyperscaling violation exponent $\theta$. Using the horizon focusing (null focusing) approach, the authors derive a general formula separating scalar and vector contributions to $\zeta/\eta$, and demonstrate how broken Lifshitz symmetry leads to nonzero bulk viscosity with distinct neutral and charged cases. They further explore running bulk viscosity in a charged, $z=1$ model with hyperscaling violation, showing how $\zeta/\eta$ interpolates between UV Lifshitz-invariant behavior and IR quasi-conformal regimes as temperature changes. Collectively, the results illuminate how bulk viscosity encodes the degree and nature of scale invariance breaking in quantum critical holographic fluids, offering a diagnostic for extracting $z$ and $\theta$ from transport data in neutral and charged systems.

Abstract

We compute the bulk viscosity in holographic models dual to theories with Lifshitz scaling and/or hyperscaling violation, using a generalization of the bulk viscosity formula derived in arXiv:1103.1657 from the null focusing equation. We find that only a class of models with massive vector fields are truly Lifshitz scale invariant, and have a vanishing bulk viscosity. For other holographic models with scalars and/or massless vector fields we find a universal formula in terms of the dynamical exponent and the hyperscaling violation exponent.