TsT vs. LCR and Gravity Dual of Non-relativistic Fluid

TL;DR

This paper compares two holographic methods for deriving non-relativistic fluids from relativistic ones, demonstrating their equivalence and providing detailed constitutive relations and transport coefficients up to second order.

Contribution

It introduces and compares light-cone reduction and TsT transformation methods for holographic non-relativistic fluids, establishing their equivalence and deriving explicit constitutive relations.

Findings

The two methods yield equivalent non-relativistic fluids up to second order.

Explicit constitutive relations for holographic U(1) charged fluids are provided.

Transport coefficients are computed up to second order in derivatives.

Abstract

We discuss two different approaches to synthesise holographic non-relativistic fluid from its relativistic counterpart. In the first approach we obtain the non-relativistic fluid by light-cone reduction of a relativistic conformal fluid. In the second approach we consider the bulk dual of the relativistic fluid, uplift the solution to 10 dimensions and perform TsT transformations on the bulk solution to change the asymptotic structure. Reducing the TsT transformed geometry over $S^5$ we find an effective 5 dimensional locally boosted solution. We then use the bulk-boundary dictionary to compute the non-relativistic constitutive relations. We show that the non-relativistic fluids obtained by these two methods are equivalent up to second order in derivative expansion. Our results also provide explicit expressions for different constitutive relations and transports of holographic $U(1)$ charged non-relativistic fluids (both parity odd and even) up to second order in derivative expansion.