Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators

TL;DR

This paper derives explicit formulas for the partition function of mass-deformed ABJ and ABJM theories at weak coupling using Meixner-Pollaczek polynomials and $su(1,1)$ oscillators, connecting matrix models with quantum algebra structures.

Contribution

It provides a novel analytical approach to compute partition functions of mass-deformed ABJ and ABJM theories using orthogonal polynomials and $su(1,1)$ algebra, including Wilson loop analysis.

Findings

Explicit partition function expressions for finite N, M, and arbitrary parameters.

Identification of the matrix model with a Meixner-Pollaczek ensemble.

Wilson loops interpreted via $su(1,1)$ coherent states.

Abstract

We give explicit analytical expressions for the partition function of $U(N)_{k}\times U(N+M)_{-k}$ ABJ theory at weak coupling ($k\rightarrow \infty )$ for finite and arbitrary values of $N$ and $M$ (including the ABJM case and its mass-deformed generalization). We obtain the expressions by identifying the one-matrix model formulation with a Meixner-Pollaczek ensemble and using the corresponding orthogonal polynomials, which are also eigenfunctions of a $su(1,1)$ quantum oscillator. Wilson loops in mass-deformed ABJM are also studied in the same limit and interpreted in terms of $su(1,1)$ coherent states.