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: $F_{ \mathbb{ S}^3_{ \varepsilon}}^{ (3)}(0)=\frac{ 1}{ 630}\pi^4 C_{ \scriptscriptstyle T} t_4$, 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: $F_{ \mathbb{ S}^5_{ \varepsilon}}^{ (3)}(0)=\frac{ 2}{ 15}\pi^6 C_{ \scriptscriptstyle T} \left[1+\frac{ 3}{ 40} t_2+\frac{ 23}{ 630} t_4\right]$. We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement.
Categories: hep-th gr-qc