Abstract
We provide general formulae for the topologically twisted index of a general three-dimensional \( \mathcal{N} \) ≥ 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 × 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 AdS4 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.
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Hosseini, S.M., Zaffaroni, A. Large N matrix models for 3d \( \mathcal{N} \) = 2 theories: twisted index, free energy and black holes. J. High Energ. Phys. 2016, 64 (2016). https://doi.org/10.1007/JHEP08(2016)064
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DOI: https://doi.org/10.1007/JHEP08(2016)064