Holographic GB gravity in arbitrary dimensions

TL;DR

This work analyzes Gauss–Bonnet gravity in AdS across arbitrary dimensions $D\ge 5$, building a precise AdS/CFT dictionary that connects bulk couplings to universal CFT data such as $C_T$ and the energy-flux parameters $t_2,t_4$. It shows that in GB gravity $t_4=0$, derives positive-energy flux bounds that translate into explicit bounds on the GB coupling $\lambda_{\text{GB}}$, and demonstrates that these flux-based constraints precisely match causality constraints from the dual CFT. The authors then study GB holographic hydrodynamics, obtaining the corrected shear-viscosity-to-entropy ratio $\eta/s$, the speed of sound, and the relaxation time $\tau_\Pi$, and analyze causality violations in second-order hydrodynamics. Across dimensions, the results illuminate how higher-curvature corrections shape transport and stability in strongly coupled plasmas, providing dimension-dependent bounds and highlighting the nuances of holographic models for QGP-like systems.

Abstract

We study the properties of the holographic CFT dual to Gauss-Bonnet gravity in general $D \ge 5$ dimensions. We establish the AdS/CFT dictionary and in particular relate the couplings of the gravitational theory to the universal couplings arising in correlators of the stress tensor of the dual CFT. This allows us to examine constraints on the gravitational couplings by demanding consistency of the CFT. In particular, one can demand positive energy fluxes in scattering processes or the causal propagation of fluctuations. We also examine the holographic hydrodynamics, commenting on the shear viscosity as well as the relaxation time. The latter allows us to consider causality constraints arising from the second-order truncated theory of hydrodynamics.

Figures (1)

• Figure 1: (Colour online) Front velocity in the sound channel. From top to bottom, the blue, green, red and purple curves correspond to $D=5$, $6$, $7$ and $8$, respectively. The dashed vertical lines indicate where this velocity reaches one on the various curves.