Higher Spin Contributions to Holographic Fluid Dynamics in $AdS_5/CFT_4$

TL;DR

This paper computes the influence of higher spin fields on holographic fluid dynamics in AdS_5/CFT_4, revealing their role in the gradient expansion and Weyl covariance of the stress tensor.

Contribution

It introduces the calculation of higher spin contributions to the graviton's beta function in AdS_5, linking higher spin algebra to conformal hydrodynamics at higher orders.

Findings

Higher spin fields affect the beta function and stress tensor structure.

Higher spin contributions ensure Weyl covariance of the stress tensor.

Gradient expansion in 4D conformal hydrodynamics is governed by higher spin algebra.

Abstract

We calculate the graviton's $\beta$-function in $AdS$ string-theoretic sigma-model, perturbed by vertex operators for Vasiliev's higher spin gauge fields in $AdS_5$. The result is given by $\beta_{mn}=R_{mn}+4T_{mn}(g,u)$ (with the AdS radius set to 1 and the graviton polarized along the $AdS_5$ boundary), with the matter stress-energy tensor given by that of conformal holographic fluid in $d=4$, evaluated at the temperature given by $T={1\over{\pi}}$. The stress-energy tensor is given by $T_{mn}={g_{mn}}+4u_mu_n+\sum_{N}T^{(N)}_{mn}$ where $u$ is the vector excitation satisfying $u^2=-1$ and $N$ is the order of the gradient expansion in the dissipative part of the tensor. We calculate the contributions up to N=2. The higher spin excitations contribute to the $\beta$-function, ensuring the overall Weyl covariance of the matter stress tensor. We conjecture that the structure of gradient expansion in $d=4$ conformal hydrodynamics at higher orders is controlled by the higher spin operator algebra in $AdS_5$.