ABJM on ellipsoid and topological strings

Understand

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.