Partition functions on slightly squashed spheres and flux parameters

Abstract

We argue that the conjectural relation between the subleading term in the small-squashing expansion of the free energy of general three-dimensional CFTs on squashed spheres and the stress-tensor three-point charge $t_4$ proposed in arXiv:1808.02052: $F_{{\mathbb{S}}_{\epsilon }^3}^{(3)}(0)=\frac{1}{630}{\pi }^4{C}_T{t}_4$, holds for an infinite family of holographic higher-curvature theories. Using holographic calculations for quartic and quintic Generalized Quasi-topological gravities and general-order Quasi-topological gravities, we identify an analogous analytic relation between such term and the charges $t_2$ and $t_4$ valid for five-dimensional theories: $F_{{\mathbb{S}}_{\epsilon }^5}^{(3)}(0)=\frac{2}{15}{\pi }^6{C}_T\left[1+\frac{3}{40}{t}_2+\frac{23}{630}{t}_4\right]$. We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement.

52 pages, 2 figures