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By compactifying gauge theories on a lower dimensional manifold, we oftenfind many interesting relationships between a geometry and a supersymmetricquantum field theory. In this paper we consider conformal field theoriesobtained from twisted compactification on a Riemann surface with a boundary.Various kinds of supersymmetric boundary conditions are exchanged underS-duality. To consider these transformations one need to take into accountboundary degrees of freedom. So we study how the degrees of freedom can beadded at the boundary of the Riemann surface. In this paper I show that thisintroduction of the boundary fields can be done preserving supersymmetry bymeans of 2-dimensional superfields.

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