Universality of squashed-sphere partition functions

TL;DR

This paper introduces a universal, UV-finite formula for calculating the free energy of odd-dimensional CFTs on squashed spheres, linking holographic and free-field results and proposing a universal relation involving stress-tensor three-point functions.

Contribution

It provides a new, simple holographic formula for free energy on squashed spheres that is UV-finite and relates to the bulk AdS vacua, also conjecturing universality of stress-tensor three-point functions.

Findings

The formula is UV-finite and involves evaluating the bulk Lagrangian on pure-AdS.

The free energy expansion's subleading term is universally controlled by the stress-tensor three-point function charge t_4.

Holographic and free-field calculations support the universality conjecture.

Abstract

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 is automatically UV-finite and only involves a simple evaluation of the corresponding bulk Lagrangian on an auxiliary pure-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.