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

Abstract

We give explicit analytical expressions for the partition function of U (N ) k × U (N + M ) −k ABJ theory at weak coupling (k → ∞) 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. 7 The one boson realization only allows for Bargmann index λ = 1/4 or λ = 3/4. 8 Thanks to Jorge Russo for pointing this out.

4d/2d → 3d/1d: A song of protected operator algebras

“…, σ r ) and σ ∨ = i σ i α ∨ i , with α ∨ i the coroots (this is simply a convenient choice of normalization of σ). For general N , such integrals are complicated and can be studied using the techniques developed in [116][117][118][119][120]. Focusing on the case N = 3, we obtain…”