Abstract
We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class mathrm{mathcal{R}} . Using results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d correspondence we are able to constrain the two independent coefficients in the four-derivative supergravity Lagrangian. This in turn allows us to calculate the subleading terms in the large-N expansion of supersymmetric partition functions for an infinite class of three-dimensional mathcal{N} = 2 SCFTs of class mathrm{mathcal{R}} . We also determine the leading correction to the Bekenstein-Hawking entropy of asymptotically AdS4 black holes arising from wrapped M5-branes. In addition, we propose and test some conjectures about the perturbative partition function of Chern-Simons theory with complexified ADE gauge groups on closed hyperbolic three-manifolds.
Highlights
We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class R
Theory compactified on S7 and using results for supersymmetric localization of 3d N = 2 SCFTs arising on the world-volume of M2-branes it was shown in [5, 6] how to determine the coefficients of these four-derivative terms
Our results amount to explicit evaluation of the leading and subleading terms in the large N expansion of various supersymmetric partition functions and the two-point function of the energy momentum tensor
Summary
Our supergravity analysis is based on two sets of results. First, we use the fact that 11d supergravity admits a consistent truncation to 4d N = 2 minimal supergravity suitable for describing the backreaction of M5-branes wrapping three-manifolds [7]. The ansatz for the supergravity background fields in this truncation is inspired by an AdS4 × H3 solution of the maximal 7d SO(5) gauged supergravity [18] found in [19] and interpreted as arising from wrapped M5-branes in [20]. This consistent truncation implies that any solution of the equations of motion of minimal 4d N = 2 gauged supergravity can be uplifted to a solution of 11d supergravity. It was shown in [5, 6] that every solution of the two-derivative equations of motion derived from the Lagrangian L2∂ in (2.2), Rμν
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