N = 4 SYM on R x S3 and theories with 16 supercharges

We study N = 4 SYM on R x S3 and theories with 16 supercharges arising as its consistent truncations. These theories include the plane wave matrix model, N = 4 SYM on R x S2 and N = 4 SYM on R x S3/Zk, and their gravity duals were studied by Lin and Maldacena. We make a harmonic expansion of the original N = 4 SYM on R x S3 and obtain each of the truncated theories by keeping a part of the Kaluza-Klein modes. This enables us to analyze all the theories in a unified way. We explicitly construct some nontrivial vacua of N = 4 SYM on R x S2. We perform 1-loop analysis of the original and truncated theories. In particular, we examine states regarded as the integrable SO(6) spin chain and a time-dependent BPS solution, which is considered to correspond to the AdS giant graviton in the original theory