On the Cardy-Verlinde Formula and the de Sitter/CFT Correspondence

TL;DR

This paper derives a version of the Cardy--Verlinde entropy formula for boundary theories in de Sitter space, linking black hole evaporation, RG flow, and the boundary CFT's properties.

Contribution

It extends the Cardy--Verlinde formula to non-conformal boundary theories in de Sitter space and relates black hole instability to RG flow dynamics.

Findings

Boundary theory has a monotonic C-function defined by Casimir energy.

Black hole evaporation corresponds to an RG flow from IR to UV.

De Sitter space endpoint is described by a conformal theory at UV fixed point.

Abstract

We derive the Cardy--Verlinde entropy formula for the field theory that lives on the boundary of an asymptotically de Sitter space with a black hole. The boundary theory which is not conformal has a monotonic $C$--function defined by the Casimir energy. The instability of the space due to Hawking radiation from the black hole corresponds to an RG flow from the IR to the UV during which $C$ increases. The endpoint of black hole evaporation is de Sitter space which is described by a conformal theory at the UV fixed point of the RG flow.