RG Flows and Thermofield-Double States in Holography

TL;DR

This paper explores the RG flow of Thermofield-Double states in holography, revealing how deformations influence the IR fixed point's position relative to the black hole horizon and its implications for holographic correlations.

Contribution

It demonstrates that the IR fixed point of the RG flow can be tuned to remain inside the black hole horizon, providing new insights into the structure of holographic RG flows and TFD states.

Findings

IR fixed point can be kept inside the black hole horizon

Fine-tuning deformation brings the fixed point close to the horizon

Correlations between TFD copies depend on the RG flow details

Abstract

In this article, we consider a Renormalization Group flow of the Thermofield-Double state in a UV-complete description of Holography, by introducing a relevant deformation to the ${\cal N}=4$ super Yang-Mills theory at strong coupling. This RG-flow is known to have a non-trivial, interacting ${\cal N}=1$ fixed point at the IR. Geometrically, an RG-flow of the TFD-state naturally continues radially and inside the black hole event horizon and yields a Kasner-structure near singularity, as has been observed in recent works. We show that for a generic value of the deformation, the putative IR fixed point remains inside the black hole. By fine-tuning this deformation, the "fixed point" can be brought arbitrarily close to the event horizon, while always remaining inside. Physically, this distinguishes between the vanishing temperature limit of the RG-flows with the one at exactly zero temperature. We further discuss its general implications in the context of Holography. We also discuss how correlations between the two-copies of the TFD-state depend on this explicit RG-flow.