Partition functions on slightly squashed spheres and flux parameters

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 (3) S 3 ε (0) = 1 630 π 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 t 2 and t 4 valid for five-dimensional theories: F (3) S 5 ε (0) = 2 15 π 6 C T 1 + 3 40 t 2 + 23 630 t 4 . We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement.ArXiv ePrint: arXiv:20xx.xxxxx

Holographic entanglement entropy for perturbative higher-curvature gravities

“…These theories define holographic toy models of non-supersymmetric CFTs in d = 4 and d = 3, respectively. Various holographic aspects of such models have been explored before e.g., in [8,9,12,13,20,21,58]. The special properties of Quasi-topological and Einsteinian cubic gravities include the fact that they possess second-order equations on maximally symmetric backgrounds, that they allow for generalizations of the Schwarzschild solution with a single function, i.e., satisfying g tt g rr = −1, as well as the fact that the associated thermodynamic properties can be computed fully analytically [59][60][61].…”

“…This extends beyond explicit top-down constructions and, in fact, particular higher-curvature models -e.g., with certain special properties which makes them more appealing -can be used to probe interesting CFT physics [7][8][9][10][11]. In some cases, this approach has been used to unveil universal properties valid for completely general CFTs [12][13][14][15][16][17][18][19][20][21].…”

Electromagnetic quasitopological gravities

“…In fact, it is known that higher-derivative gravities with a negative cosmological constant are very useful holographic toy models that can be used to learn non-trivial information about Conformal Field Theories -see refs. [59,67] for recent results involving Generalized Quasitopological gravities. Since EGQGs contain higher-derivatives not only of the metric but also of a vector field, these may be used to probe additional aspects of a CFT.…”

“…The situation is different for asymptotically AdS solutions, but in that case one may introduce an effective boundary term which is proportional to the Gibbons-Hawking-York term[58]. This procedure is known to work at least for theories of the GQG class and has been tested in several occasions[44,59,67].…”

Does the round sphere maximize the free energy of (2+1)-dimensional QFTs?

“…This is feature is interestingly reminiscent of the results of [9], which study the free energy of the massless Dirac fermion, the conformally coupled scalar, and holographic CFTs on a squashed Euclidean three-sphere; they found that for small and modest squashings, the free energies of all of these theories agree more closely than should be expected from CFT considerations alone. Indeed, there is a conjecture and good evidence that the subleading term in the perturbative expansion of the free energy in the squashing parameter, determined by the three-point function of the stress tensor, is surprisingly universal for all three-dimensional CFTs [28,29]. In fact, this theory-independence becomes exact in a long-wavelength limit.…”