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

• Main Author: Tomoki Nosaka
• Format: Article
• Language: English
• Published: SpringerOpen 2021-06-01
• Series: Journal of High Energy Physics
• Subjects: Chern-Simons Theories; M-Theory; Matrix Models; Supersymmetric Gauge Theory
• Online Access: https://doi.org/10.1007/JHEP06(2021)060

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 N $$ \mathcal{N} $$ = 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 m 1 = m 2 = −πi(ν − 2a)/ν, the bilinear relation corresponds to the q-deformation of the affine SU(ν) Toda equation in τ-form.