Universality of Squashed-Sphere Partition Functions

We present several results concerning the free energy of odd-dimensional conformal field theories (CFTs) on squashed spheres. First, we propose a formula which computes this quantity for holographic CFTs dual to higher-curvature gravities with second-order linearized equations of motion. As opposed...

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Bibliographic Details
Published in:Physical review letters 2019-02, Vol.122 (7), p.071602-071602, Article 071602
Main Authors: Bueno, Pablo, Cano, Pablo A, Hennigar, Robie A, Mann, Robert B
Format: Article
Language:English
Subjects:
Curvature
Equations of motion
Free energy
Functionals
Partitions (mathematics)
Tensors
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Summary:We present several results concerning the free energy of odd-dimensional conformal field theories (CFTs) on squashed spheres. First, we propose a formula which computes this quantity for holographic CFTs dual to higher-curvature gravities with second-order linearized equations of motion. As opposed to standard on-shell action methods for Taub geometries, our formula only involves a simple evaluation of the corresponding bulk Lagrangian on an auxiliary pure anti-de Sitter (AdS) space. The expression is closely related to the function determining the possible AdS vacua of the bulk theory in question, which we argue to act as a generating functional from which correlation functions of the boundary stress tensor can be easily characterized. Finally, based on holographic results and free-field numerical calculations, we conjecture that the subleading term in the squashing-parameter free-energy expansion is universally controlled by the stress-tensor three-point function charge t_{4} for general (2+1)-dimensional CFTs.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.122.071602