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

TL;DR

This paper develops new bilinear relations for the ABJ theory's partition functions with mass deformations, enabling recursive exact calculations and exploring large N asymptotics beyond previous small-mass approximations.

Contribution

It introduces generalized bilinear relations for mass-deformed ABJ partition functions, improving computational efficiency and extending large N analysis beyond small-mass regimes.

Findings

Derived new bilinear relations for partition functions.

Enabled recursive exact calculations using dualities.

Analyzed large N asymptotics in supercritical mass regime.

Abstract

We find new bilinear relations for the partition functions of U(N)_k x 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.