Free energy dependence on spatial geometry for (2+1)-dimensional QFTs

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Title: Free energy dependence on spatial geometry for (2+1)-dimensional QFTs
Authors: Cheamsawat, K
Wallis, L
Wiseman, T
Item Type: Journal Article
Abstract: We consider (2+1)-QFT at finite temperature on a product of time with a static spatial geometry. The suitably defined difference of thermal vacuum free energy for the QFT on a deformation of flat space from its value on flat space is a UV finite quantity, and for reasonable fall-off conditions on the deformation is IR finite too. For perturbations of flat space we show this free energy difference goes quadratically with perturbation amplitude and may be computed from the linear response of the stress tensor. As an illustration we compute it for a holographic CFT finding that at any temperature, and for any perturbation, the free energy decreases. Similar behaviour was previously found for free scalars and fermions, and for unitary CFTs at zero temperature, suggesting (2+1)-QFT may generally energetically favour a crumpled spatial geometry. We also treat the deformation in a hydrostatic small curvature expansion relative to the thermal scale. Then the free energy variation is determined by a curvature correction to the stress tensor and for these theories is negative for small curvature deformations of flat space.
Issue Date: 11-Sep-2019
Date of Acceptance: 24-Jul-2019
ISSN: 0264-9381
Publisher: IOP Publishing
Journal / Book Title: Classical and Quantum Gravity
Volume: 36
Issue: 19
Copyright Statement: © 2019 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at
Keywords: hep-th
02 Physical Sciences
01 Mathematical Sciences
Nuclear & Particles Physics
Notes: 24 pages, 1 figure
Publication Status: Published
Embargo Date: 2020-07-25
Online Publication Date: 2019-07-25
Appears in Collections:Physics
Theoretical Physics

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