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: {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}_{{mathbbm{S}}_{varepsilon}^5}^{(3)}(0)=frac{2}{15}{pi}^6{C}_Tleft[1+frac{3}{40}{t}_2+frac{23}{630}{t}_4right] . We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement.
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