D-brane field theory on compact spaces

TL;DR

This paper develops a gauge theory framework for D-branes in toroidally compactified spaces, explicitly incorporating winding modes and demonstrating T-duality equivalence with dual brane systems.

Contribution

It provides an explicit construction of the field theory for D-branes on compact spaces, including winding modes, and shows T-duality correspondence.

Findings

Constructed gauge theory with winding modes on compact spaces.

Demonstrated T-duality equivalence between winding and momentum modes.

Extended the understanding of D-brane dynamics in compactified string theory.

Abstract

We consider Dirichlet p-branes in type II string theory on a space which has been toroidally compactified in d dimensions. We give an explicit construction of the field theory description of this system by putting a countably infinite number of copies of each brane on the noncompact covering space, and modding out the resulting gauge theory by Z^d. The resulting theory is a gauge theory with graded fields corresponding to strings winding around the torus an arbitrary number of times. In accordance with T-duality, this theory is equivalent to the gauge theory for the dual system of (d + p)-branes wrapped around the compact directions, where the winding number is exchanged for momentum in the compact direction.