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.

• Received 27 August 2018
• Revised 15 January 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.071602

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Published by the American Physical Society