Abstract
We apply the technique of supersymmetric localization to exactly compute the S 5 partition function of several large N superconformal field theories in five dimensions that have AdS6 duals in massive type IIA supergravity. The localization computations are performed in the non-renormalizable effective field theories obtained through relevant deformations of the UV superconformal field theories. We compare the S 5 free energy to a holographic computation of entanglement entropy in the AdS6 duals and find perfect agreement. In particular, we reproduce the N 5/2 scaling of the S 5 free energy that was expected from supergravity.
Highlights
JHEP05(2014)032 such theories, it was possible to match the S3 free energy predicted from the gravity side with a field theory computation, and in particular to reproduce the N 3/2 scaling using just field theory methods [15,16,17,18,19]
From the massive type IIA supergravity backgrounds dual to the UV SCFTs one expects the number of degrees of freedom to scale as N 5/2 at large N [25], but explicit formulas for the free energy on S5, F = − log |ZS5|, have not been determined
Unlike in 3d where the strongly-coupled SCFT is in the deep IR, and one can perform localization in a weakly-coupled UV theory that flows in the IR to the SCFT of interest, in 5d the strongly-coupled SCFT is at the UV fixed point
Summary
The five-dimensional superconformal theories we will examine lack a Lagrangian description at the conformal fixed point. One may deform these theories by a relevant operator, such that in the IR they flow to 5d N = 1 Yang-Mills coupled to various hyper multiplets [26]. As shown in [23] (see [21, 22] for earlier work and [40]), the S5 partition function of 5d Yang-Mills theory with gauge group G and matter hyper multiplets in representations Ri takes the form. The function F (σ) knows about the U(1)r gauge theory on the Coulomb branch, where r is the rank of the gauge group It encodes the effective CS level and the effective gauge coupling, which are given, respectively, by the third and second derivatives of the prepotential.
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