The one-loop vacuum energy and RG flow induced by double-trace operators in AdS/CFT and dS/CFT correspondence

TL;DR

This paper investigates one-loop vacuum energy differences in AdS and dS spaces caused by double-trace operators, revealing RG flow, phase transitions, and c-function behavior consistent with c-theorem in various gravitational backgrounds.

Contribution

It extends the analysis of vacuum energy differences and RG flow induced by double-trace operators to AdS black holes and deSitter space, including phase transition and c-function behavior.

Findings

Vacuum energy differences specify boundary conditions related to double-trace operators.

Instability in AdS black holes indicates Hawking-Page phase transition.

c-function exhibits monotonic behavior beyond leading order, aligning with c-theorem.

Abstract

We calculate the difference of one-loop vacuum energies for massive scalar field in five-dimensional AdS black hole. (The same is done in five-dimensional deSitter space). In each case this difference is specified by the boundary conditions corresponding to the double-trace operator (massive term) and it describes RG flow in the manner discussed by Gubser-Mitra for pure AdS space. For AdS black hole there occurs instability which is the manifestation of the Hawking-Page phase transition. For stable phase of AdS black hole as well as for deSitter bulk, c-function found beyond the leading order approximation shows the monotonic behaviour consistent with c-theorem.