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

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Publication date: 12 June 2018

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Abstract: We provide general formulae for the topologically twisted index of a general three-dimensional $calNgeq2$ 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 $S^{2}imes{S}^1$ 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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