Duality symmetry of N= 4 Yang-Mills theory on T3 Original Research Article

We study the spectrum of BPS states in N = 4 supersymmetric U(N) Yang-Mills theory. This theory has been proposed to describe M-theory on T3 in the discrete light-cone formalism. We find that the degeneracy of irreducible BPS bound states in this mode] exhibits a (partially hidden) SL(5, Z) duality symmetry. Besides the electro-magnetic symmetry, this duality group also contains Nahm-like transformations that interchange the rank N of the gauge group with some of the magnetic or electric fluxes. In the M-theory interpretation, this mapping amounts to a reflection that interchanges the longitudinal direction with one of the transverse directions.