D-brane field theory on compact spaces

A low-energy field theory is constructed for Dirichlet p-branes in type II string theory on a space which has been toroidally compactified in d transverse dimensions. This field theory is found by taking a Zd quotient of a theory describing a countably infinite set of branes on the covering space. In accordance with T-duality, the resulting theory is equivalent to the gauge theory for the dual system of (d + p)-branes wrapped around the compact directions.