We study theories with SU(2|4) symmetry, which include the plane wave matrix model, 2+1 SYM on R × S2 and Script N = 4 SYM on R × S3/Zk. 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 R × S2 and Script N = 4 SYM on R × S3/Zk 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 S3, 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.
Journal of High Energy Physics
- Pub Date:
- November 2006
- High Energy Physics - Theory
- 56 pages, 6 figures, v2:a footnote and references added, section 5.2 improved, typos corrected, v3:typos corrected