RG flows and thermofield-double states in holography

Abstract

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 N $$ \mathcal{N} $$ = 4 super Yang-Mills theory at strong coupling. This RG-flow is known to have a non-trivial, interacting N $$ \mathcal{N} $$ = 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 in a certain sense. 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, including a study of the recently-proposed Holographic a-function, especially in the interior of the black hole. We also discuss how correlations between the two-copies of the TFD-state depend on this explicit RG-flow.

Keywords

• AdS-CFT Correspondence
• Black Holes
• Renormalization Group
• Supergravity Models