Abstract
Abstract
We study the large N limit of some supersymmetric partition functions of the U(N)k × U(N)−k ABJM theory computed by supersymmetric localization. We conjecture an explicit expression, valid to all orders in the large N limit, for the partition function on the U(1) × U(1) invariant squashed sphere in the presence of real masses in terms of an Airy function. Several non-trivial tests of this conjecture are presented. In addition, we derive an explicit compact expression for the topologically twisted index of the ABJM theory valid at fixed k to all orders in the 1/N expansion. We use these results to derive the topologically twisted index and the sphere partition function in the ’t Hooft limit which correspond to genus g type IIA string theory free energies to all orders in the α′ expansion. We discuss the implications of our results for holography and the physics of AdS4 black holes.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
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