S-Duality for Intersecting D3-Branes

Although S-duality is an immensely useful tool in the study of quantum field theory, an explicit derivation of the duality does not exist for most non-trivial theories.  With the goal of better understanding a path integral derivation of S-duality, we study the defect gauge theory that lives on two perpendicular D3-branes with a 1+1 dimensional intersection.  We show that S-duality in this theory may be realized by the composition of two T-dualities with an electromagnetic duality that exchanges the electric and magnetic fields on the branes.  The T-dual’ed circle, which is in the field space of the intersection scalars, does not conserve winding number and thus maps to a circle on which momentum is not conserved.  The problem of deriving S-duality in this theory then reduces to the known problem of performing a T-duality on a circle that lacks a continuous isometry.