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 \( {\mathbb{F}}_0 \). 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 CalabiYau threefold, known as local \( {\mathrm{\mathbb{P}}}^2 \). 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 Rényi entropy.
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Hatsuda, Y. ABJM on ellipsoid and topological strings. J. High Energ. Phys. 2016, 26 (2016). https://doi.org/10.1007/JHEP07(2016)026
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DOI: https://doi.org/10.1007/JHEP07(2016)026