Generalized complexes and string field theory

TL;DR

This paper develops a mathematical framework for open string field theory with D-branes, showing how to extend the theory to include all D-brane composites and achieve a unitarily complete description.

Contribution

It introduces a minimal extension of the D-brane category using generalized complexes, ensuring closure under D-brane composite formation in string field theory.

Findings

The extended D-brane category is closed under composite formation.

A weak unitarity constraint is formulated and satisfied.

The framework provides a general description of D-brane composites in string theory.

Abstract

I discuss the axiomatic framework of (tree-level) associative open string field theory in the presence of D-branes by considering the natural extension of the case of a single boundary sector. This leads to a formulation which is intimately connected with the mathematical theory of differential graded categories. I point out that a generic string field theory as formulated within this framework is not closed under formation of D-brane composites and as such does not allow for a unitary description of D-brane dynamics. This implies that the collection of boundary sectors of a generic string field theory with D-branes must be extended by inclusion of all possible D-brane composites. I give a precise formulation of a weak unitarity constraint and show that a minimal extension which is unitary in this sense can always be obtained by promoting the original D-brane category to an enlarged category constructed by using certain generalized complexes of D-branes. I give a detailed construction of this extension and prove its closure under formation of D-brane composites. These results amount to a completely general description of D-brane composite formation within the framework of associative string field theory.