Two-dimensional superconformal field theories from Riemann surfaces with boundary

We consider a 2-dimensional conformal field theory (CFT) obtained from twisted compactification of the 4-dimensional N=4 super Yang-Mills theory on a Riemann surface with boundary. We find the boundary conditions to preserve some of the supersymmetry. In particular an N=(2,2) superconformal field theory is obtained from supersymmetry breaking due to the boundary from N=(4,4). In this case we calculate the central charge of the CFT and show its dependence on the topology of the Riemann surface.