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Vacuum energy is non-positive for (2 + 1)-dimensional holographic CFTs

Hickling, Andrew, Wiseman, Toby·2016·Classical and Quantum Gravity
DOI 10.1088/0264-9381/33/4/045009
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Abstract

We consider a (2 + 1)-dimensional holographic CFT on a static spacetime with globally timelike Killing vector. Taking the spatial geometry to be closed but otherwise general we expect a non-trivial vacuum energy at zero temperature due to the Casimir effect. We assume a thermal state has an AdS/CFT dual description as a static smooth solution to gravity with a negative cosmological constant, which ends only on the conformal boundary or horizons. A bulk geometric argument then provides an upper bound on the ratio of CFT free energy to temperature. Considering the zero temperature limit of this bound implies the vacuum energy of the CFT is non-positive. Furthermore the vacuum energy must be negative unless the boundary metric is locally conformal to a product of time with a constant curvature space. We emphasise the argument does not require the zero temperature bulk geometry to be smooth, but only that singularities are ‘good’ so are hidden by horizons at finite temperature.

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Cited by

Metadata

Authors
Hickling, A., & Wiseman, T.
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
2016-01-27
Volume
33
Issue
4
Pages
045009
ISSN
  • 0264-9381
  • 1361-6382
DOI
10.1088/0264-9381/33/4/045009
Cited by
11
References
0
Licence
Funders
Science and Technology Facilities Council (ST/J0003533/1)

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