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

Abstract

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). The predictions of S-duality (which commutes with the mapping class group) are fulfilled as expected, but the proof requires some surprisingly intricate combinatorial infinite product identities.

17 pages

References in corpus (3)

• Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections, bound states at threshold, and S-duality
• Bound states in N = 4 SYM on T^3: Spin(2n) and the exceptional groups
• A note on S-duality for the N=1* Sp(2n) and SO(2n+1) super-Yang-Mills theories

Cited by in corpus (4)

• BPS states in (2,0) theory on R x T5
• Rigid surface operators and S-duality: some proposals
• Rigid Surface Operator and Symbol Invariant of Partitions
• Finite energy shifts in SU(n) supersymmetric Yang-Mills theory on T^3xR at weak coupling