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 t4 proposed in arXiv:1808.02052: FSε3(3)(0)=1630π4CTt4, 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 t2 and t4 valid for five-dimensional theories: FSε5(3)(0)=215π6CT[1+340t2+23630t4]. We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement.