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arXiv · 2001.10020

Partition functions on slightly squashed spheres and flux parameters

Pablo Bueno·Pablo A. Cano·Robie A. Hennigar·Victor A. Penas·Alejandro Ruipérez
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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: $F_{\mathbb{S}^3_{\varepsilon}}^{(3)}(0)=\frac{1}{630}\pi^4 C_{\scriptscriptstyle T} t_4$, 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.

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Pablo Bueno, Pablo A. Cano, Robie A. Hennigar, Victor A. Penas, Alejandro Ruipérez. 2020-01-27. Partition functions on slightly squashed spheres and flux parameters. https://doi.org/10.1007/jhep04(2020)123

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