Construction of 4d SYM compactified on open Riemann surfaces by the superfield formalism

By compactifying gauge theories on a lower dimensional manifold, we often find many interesting relationships between a geometry and a supersymmetric quantum field theory. In this paper we consider conformal field theories obtained from twisted compactification on a Riemann surface with a boundary. Various kinds of supersymmetric boundary conditions are exchanged under S-duality. To consider these transformations one need to take into account boundary degrees of freedom. So we study how the degrees of freedom can be added at the boundary of the Riemann surface. In this paper I show that this introduction of the boundary fields can be done preserving supersymmetry by means of 2-dimensional superfields.