Exact results for perturbative partition functions of theories with SU(2|4) symmetry

TL;DR

This paper applies localization to SU(2|4) symmetric theories, deriving exact perturbative partition functions for PWMM, SYM on R×S^2, and SYM on R×S^3/Z_k, and proves large-N reduction for certain operators.

Contribution

It provides the first exact perturbative matrix integral expressions for these theories using localization, connecting PWMM, SYM on R×S^2, and R×S^3/Z_k.

Findings

Derived matrix integrals for PWMM, SYM on R×S^2, and R×S^3/Z_k.

Provided a nonperturbative proof of large-N reduction for Wilson loops and free energy.

Demonstrated the perturbative part of these theories exactly, ignoring instanton effects.

Abstract

In this paper, we study the theories with SU(2|4) symmetry which consist of the plane wave matrix model (PWMM), super Yang-Mills theory (SYM) on RxS^2 and SYM on RxS^3/Z_k. The last two theories can be realized as theories around particular vacua in PWMM, through the commutative limit of fuzzy sphere and Taylor's T-duality. We apply the localization method to PWMM to reduce the partition function and the expectation values of a class of supersymmetric operators to matrix integrals. By taking the commutative limit and performing the T-duality, we also obtain the matrix integrals for SYM on RxS^2 and SYM on RxS^3/Z_k. In this calculation, we ignore possible instanton effects and our matrix integrals describe the perturbative part exactly. In terms of the matrix integrals, we also provide a nonperturbative proof of the large-N reduction for circular Wilson loop operator and free energy in N=4 SYM on RxS^3.