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Partition functions on squashed seven-spheres and holography. (arXiv:2211.13516v2 [hep-th] UPDATED)

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Our paper presents two main results. First, we study the renormalized free
energies of Euclidean Einstein gravity in asymptotically AdS$_8$ and various
field theories on a squashed seven sphere. In the gravity theory, we
demonstrate the absence of the Hawking-Page transition, while in the field
theory, we focus on the O($N$) vector model and the massless free fermion
model. The conformal symmetry governs the universal behaviors of the free
energies for small and large squashings, which we confirm numerically and
analytically. Second, we evaluate the second-order derivative of CFT free
energy with respect to the squashing parameter, finding universal results that
hold for generic conformal field theories. We examine two different squashings,
one with an SU(2) bundle, which is the primary focus of our paper, and another
with a U(1) bundle, where our results align with the conjectured formula from
the gravity side in the literature.

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