Physics Group Meeting

Non-abelian maximally supersymmetric Yang-Mills theory on a flat spatial three-torus has an intricate structure of normalizable zero-energy states, characterized by their values of the discrete abelian electric and magnetic 't Hooft fluxes, and by their behavior under the mapping class group of the three-torus. S-duality transforms the 't Hooft fluxes as a doublet, and commutes with the mapping class group. It thus imposes strong constraints on the spectra of vacuum states for theories with dual gauge groups. This is however far from manifest in the present formulation of the theory. These predictions of S-duality can be checked explicitly by exploiting their invariance under smooth deformations of the theory, and carrying out the computations in the weak coupling limit. The cases when the gauge group belongs to one of the infinite series of classical matrix groups are particularly intriguing, and lead to amusing combinatorial identities related to certain infinite products.