SU(N) q-Toda equations from mass deformed ABJM theory

Abstract

Abstract It is known that the partition functions of the U(N)k × U(N + M)−k ABJM theory satisfy a set of bilinear relations, which, written in the grand partition function, was recently found to be the q-Painlevé III3 equation. In this paper we have suggested that a similar bilinear relation holds for the ABJM theory with $$ \mathcal{N} $$ N = 6 preserving mass deformation for an arbitrary complex value of mass parameter, to which we have provided several non-trivial checks by using the exact values of the partition function for various N, k, M and the mass parameter. For particular choices of the mass parameters labeled by integers ν, a as m1 = m2 = −πi(ν − 2a)/ν, the bilinear relation corresponds to the q-deformation of the affine SU(ν) Toda equation in τ-form.