On thermal holographic RG flows

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 thermal states. Using the Hamilton-Jacobi formalism for the coupled system, we derive the Ward identity associated with broken dilatation symmetry in thermal correlators and obtain the modified Callan-Symanzik equation for the dual thermal CFT. We then employ the Hamiltonian approach to analyze the black hole interior and comment on the near-singularity behavior from this perspective.