| Summary: | 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 S ε 3 3 0 = 1 630 π 4 C T t 4 $$ {F}_{{\mathbbm{S}}_{\varepsilon}^3}^{(3)}(0)=\frac{1}{630}{\pi}^4{C}_T{t}_4 $$ , 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 t2 and t4 valid for five-dimensional theories: F S ε 5 3 0 = 2 15 π 6 C T 1 + 3 40 t 2 + 23 630 t 4 $$ {F}_{{\mathbbm{S}}_{\varepsilon}^5}^{(3)}(0)=\frac{2}{15}{\pi}^6{C}_T\left[1+\frac{3}{40}{t}_2+\frac{23}{630}{t}_4\right] $$ . We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement.
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