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: \( {F}_{{\mathbbm{S}}_{\varepsilon}^5}^{(3)}(0)=\frac{2}{15}{\pi}^6{C}_T\left[1+\frac{3}{40}{t}_2+\frac{23}{630}{t}_4\right] \). We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement.
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Bueno, P., Cano, P.A., Hennigar, R.A. et al. Partition functions on slightly squashed spheres and flux parameters. J. High Energ. Phys. 2020, 123 (2020). https://doi.org/10.1007/JHEP04(2020)123
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DOI: https://doi.org/10.1007/JHEP04(2020)123