Large N expansion of mass deformed ABJM matrix model: M2-instanton condensation and beyond

A bstract We find new bilinear relations for the partition functions of the U( N ) k × U( N + M ) −k ABJ theory with two parameter mass deformation ( m 1 , m 2 ), which generalize the q -Toda-like equation found previously for m 1 = m 2 . By combining the bilinear relations with the Seiberg-like dualities and the duality cascade relations, we can determine the exact values of the partition functions recursively with respect to N . This method is more efficient than the exact calculation by the standard TBA-like approach in the Fermi gas formalism. As an application we study the large N asymptotics of the partition function with the mass parameters in the supercritical regime where the large N expansion obtained for small mass parameters is invalid.