ABJM on ellipsoid and topological strings

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.