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

Nojiri, Shin'ichi; Odintsov, Sergei D.

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

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Nojiri, Shin'ichi
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Nojiri, S., & Odintsov, S. D. (2004). The one-loop vacuum energy and RG flow induced by double-trace operators in AdS/CFT and dS/CFT correspondence. Physical Review D, 69(2): 023511.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5093-6

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 fivedimensional 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.