N=4 SYM on R x S^3 and Theories with 16 Supercharges

TL;DR

This paper explores N=4 SYM on R x S^3 and related theories with 16 supercharges, using harmonic expansion to analyze their vacua, 1-loop effects, and connections to gravity duals, unifying various truncations.

Contribution

It provides a unified harmonic analysis framework for N=4 SYM on R x S^3 and its truncations, including explicit vacua and 1-loop effects, linking to gravity duals and integrable models.

Findings

Constructed nontrivial vacua of N=4 SYM on R x S^2

Performed 1-loop analysis of original and truncated theories

Linked states to gravity duals like AdS giant gravitons

Abstract

We study N=4 SYM on R x S^3 and theories with 16 supercharges arising as its consistent truncations. These theories include the plane wave matrix model, N=4 SYM on R x S^2 and N=4 SYM on R x S^3/Z_k, and their gravity duals were studied by Lin and Maldacena. We make a harmonic expansion of the original N=4 SYM on R x S^3 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 S^2. 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.