Self-Dual Superstring in Six Dimensions

A free superstring with chiral N=2 supersymmetry in six dimensions is proposed. It couples to a two-form gauge field with a self-dual field strength. Compactification to four dimensions on a two-torus gives a strongly coupled N=4 four-dimensional gauge theory with SL(2, Z) duality and an infinite tower of dyons. Various authors have suggested that this string theory should be also the world-volume theory of M theory five-branes. Accepting this proposal, we find a puzzling factor of two in the application to black-hole entropy computations.