ABJM on ellipsoid and topological strings

TL;DR

This paper extends the understanding of ABJM theory by analyzing its partition function on an ellipsoid with deformation parameter b, revealing a new relation to topological strings on different Calabi-Yau manifolds and providing the first complete large N solution on a squashed sphere.

Contribution

It uncovers a novel relation between the ellipsoid partition function of ABJM theory at specific parameters and topological string models on local P^2, offering the first full large N solution on a squashed sphere.

Findings

Established a relation between ABJM on ellipsoid and topological string on local P^2.

Computed the full large N expansion of the partition function for specific b values.

Analyzed supersymmetric Renyi entropy using the new results.

Abstract

It is known that the large N expansion of the partition function in ABJM theory on a three-sphere is completely determined by the topological string on local Hirzebruch surface F_0. In this note, we investigate the ABJM partition function on an ellipsoid, which has a conventional deformation parameter b. Using 3d mirror symmetry, we find a remarkable relation between the ellipsoid partition function for b^2=3 (or b^2=1/3) in ABJM theory at k=1 and a matrix model for the topological string on another Calabi-Yau threefold, known as local P^2. As in the case of b=1, we can compute the full large N expansion of the partition function in this case. This is the first example of the complete large N solution in ABJM theory on the squashed sphere. Using the obtained results, we also analyze the supersymmetric Renyi entropy.