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

  • Seyed Morteza Hosseini
  • Alberto ZaffaroniEmail author
Open Access
Regular Article - Theoretical Physics

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.

Keywords

AdS-CFT Correspondence Black Holes in String Theory M-Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Dipartimento di FisicaUniversità di Milano-BicoccaMilanoItaly
  2. 2.INFN — Sezione di Milano-BicoccaMilanoItaly

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