Higher-derivative supergravity, wrapped M5-branes, and theories of class $$ \mathrm{\mathcal{R}} $$
Nikolay Bobev, Anthony M. Charles, Dongmin Gang, Kiril Hristov, Valentin Reys
Abstract
A bstract We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class $$ \mathrm{\mathcal{R}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℛ</mml:mi> </mml:math> . 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 SCFTs of class $$ \mathrm{\mathcal{R}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℛ</mml:mi> </mml:math> . We also determine the leading correction to the Bekenstein-Hawking entropy of asymptotically AdS 4 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.