On thermal holographic RG flows

Abstract

Holographic Renormalization Group (RG) flows, described by Einstein gravity coupled to matter fields, have been thoroughly explored in the context of vacuum states. In this work, we shift the focus to \emph{thermal} states. We develop the Hamilton-Jacobi functional up to \emph{second order} in the boundary derivative expansion. Using this formalism, we derive the Ward identity associated with broken dilatation symmetry for thermal correlators. Furthermore, we also obtain the modified Callan-Symanzik equation for the dual thermal CFT. We then employ the Hamiltonian constraint approach to analyze the black hole interior and comment on the near-singularity behavior from this perspective.

arXiv comment49 pages, 1 figure