Embedding of theories with SU(2|4) symmetry into the plane wave matrix model

TL;DR

This paper demonstrates how theories with SU(2|4) symmetry, including the plane wave matrix model and certain supersymmetric Yang-Mills theories, are embedded within the plane wave matrix model, revealing harmonic relationships and extending T-duality.

Contribution

It provides a direct gauge theory proof of the embedding of 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k into the plane wave matrix model, extending T-duality to spherical geometries.

Findings

Confirmed the embedding of specific SYM theories into the plane wave matrix model.

Revealed relationships among spherical, monopole, and fuzzy sphere harmonics.

Extended T-duality to compactifications on spheres.

Abstract

We study theories with SU(2|4) symmetry, which include the plane wave matrix model, 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k. All these theories possess many vacua. From Lin-Maldacena's method which gives the gravity dual of each vacuum, it is predicted that the theory around each vacuum of 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k is embedded in the plane wave matrix model. We show this directly on the gauge theory side. We clearly reveal relationships among the spherical harmonics on S^3, the monopole harmonics and the harmonics on fuzzy spheres. We extend the compactification (the T-duality) in matrix models a la Taylor to that on spheres.