Large \(N\) matrix models for 3d \( \mathcal{N} =2\) theories: twisted index, free energy and black holes

DOI10.1007/JHEP08(2016)064zbMATH Open1390.83345arXiv1604.03122WikidataQ64038303 ScholiaQ64038303MaRDI QIDQ1639035

Author name not available (Why is that?)

Publication date: 12 June 2018

Published in: (Search for Journal in Brave)

Abstract: We provide general formulae for the topologically twisted index of a general three-dimensional

c a l N g e q 2

gauge theory with an M-theory or massive type IIA dual in the large

N

limit. The index is defined as the supersymmetric path integral of the theory on

S^{2} i m e s S^{1}

in the presence of background magnetic fluxes for the R- and global symmetries and it is conjectured to reproduce the entropy of magnetically charged static BPS AdS

_{4}

black holes. For a class of theories with an M-theory dual, we show that the logarithm of the index scales indeed as

N^{3 / 2}

(and

N^{5 / 3}

in the massive type IIA case). We find an intriguing relation with the (apparently unrelated) large

N

limit of the partition function on

S^{3}

. We also provide a universal formula for extracting the index from the large

N

partition function on

S^{3}

and its derivatives and point out its analogy with the attractor mechanism for AdS black holes.

Full work available at URL: https://arxiv.org/abs/1604.03122

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