Freelance Fluid/Gravity Correspondence, 3d Analysis

TL;DR

This paper extends the gauge/gravity correspondence to a freelance holography framework, analyzing 2d fluid dynamics in 3d Einstein gravity, and proves the $v_g$-theorem regarding fluid wave velocities along the RG flow.

Contribution

It introduces the concept of freelance fluid/gravity correspondence, providing detailed analysis of 2d fluid behavior and boundary conditions, and establishes the $v_g$-theorem for RG flow.

Findings

Proves the $v_g$-theorem for fluid wave velocities.

Analyzes the 2d fluid in 3d Einstein gravity with integrability.

Studies various boundary conditions and their effects.

Abstract

Freelance holography program is an extension of gauge/gravity correspondence, where the gravity theory is defined on a portion of AdS with an arbitrary timelike boundary, with any desired boundary conditions. It is also known that gauge/gravity correspondence admits a fluid/gravity correspondence limit, where the gauge theory side is well described by a fluid. In this work, combining the two, we work through ``freelance fluid/gravity''. In particular, we study in detail the 2d fluid (3d Einstein gravity) case, where one has a good analytical control over the bulk equations due to their integrability and absence of viscosity in the 2d fluid. We study consistency and validity requirements for the freelance fluid/gravity and how the fluid changes along the renormalization group (RG) flow. We prove the $v_g$-theorem, stating that the group velocity of fluid waves $v_g$ is a decreasing function as we move toward the infrared region along the RG flow, regardless of the adopted boundary conditions. We also study examples of holographic fluid with various asymptotic boundary conditions.