Abstract:

We consider the reduction along two compact directions of a twisted N=4 gauge theory on a 4-dimensional orientable manifold which is not a global product of two surfaces but contains a non-orientable surface. The low energy theory is a sigma-model on a 2-dimensional worldsheet with a boundary which lives on branes constructed from the Hitchin moduli space of the non-orientable surface. We verify the mirror symmetry of branes as predicted by the S-duality in gauge theory.