D-Branes in Topological Membranes

TL;DR

This paper explores how D-branes emerge in topological membrane theories, linking boundary states, orbifold relations, and gauge invariance, and demonstrating their tension arises dynamically through scalar field coupling.

Contribution

It introduces a framework for deriving D-brane boundary states and vertex operators from three-dimensional topological gauge theories with orbifold relations and matter coupling.

Findings

D-brane states are represented by vacuum wavefunctionals in gauge theories.

Boundary conditions and constraints like the Cardy condition are derived from orbifold and gauge invariance.

D-brane tension is generated dynamically via coupling to a massless scalar field.

Abstract

It is shown how two-dimensional states corresponding to D-branes arise in orbifolds of topologically massive gauge and gravity theories. Brane vertex operators naturally appear in induced worldsheet actions when the three-dimensional gauge theory is minimally coupled to external charged matter and the orbifold relations are carefully taken into account. Boundary states corresponding to D-branes are given by vacuum wavefunctionals of the gauge theory in the presence of the matter, and their various constraints, such as the Cardy condition, are shown to arise through compatibility relations between the orbifold charges and bulk gauge invariance. We show that with a further conformally-invariant coupling to a dynamical massless scalar field theory in three dimensions, the brane tension is naturally set by the bulk mass scales and arises through dynamical mechanisms. As an auxilliary result, we show how to describe string descendent states in the three-dimensional theory through the construction of gauge-invariant excited wavefunctionals.