Large N superconformal indices for 3d holographic SCFTs
Nikolay Bobev, Sunjin Choi, Junho Hong, Valentin Reys
Abstract
A bstract We study a limit of the superconformal index of the ABJM theory on S 1 × S 2 in which the size of the circle is much smaller than the radius of the two-sphere. We derive closed form expressions for the two leading terms in this Cardy-like limit which are valid to all orders in the 1 /N expansion. These results are facilitated by a judicious rewriting of the superconformal index which establishes a connection with the Bethe Ansatz Equations that control the topologically twisted index. Using the same technique we extend these results to the superconformal index of another holographic theory: 3d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> = 4 SYM coupled to one adjoint and N f fundamental hypermultiplets. We discuss the implications of our results for holography and the physics of charged rotating black holes in AdS 4 .