Zero-energy states of N = 4 SYM on T^3: S-duality and the mapping class group

Understand

We continue our studies of the low-energy spectrum of N=4 super-Yang-Mills theory on a spatial three-torus.

• In two previous papers, we computed the spectrum of normalizable zero-energy states for all choices of gauge group and all values of the electric and magnetic 't Hooft fluxes, and checked its invariance under the SL_2(Z) S-duality group.
• In this paper, we refine the analysis by also decomposing the space of bound states into irreducible unitary representations of the SL_3(Z) mapping class group of the three-torus.
• We perform a detailed study of the S-dual pairs of theories with gauge groups Spin(2n+1) and Sp(2n).