Tachyon Condensation on Orbifolds and McKay Correspondence

TL;DR

This paper explores the mathematical interpretation of tachyon condensation on orbifolds using boundary string field theory, linking decay modes in brane systems to the McKay correspondence and derived categories.

Contribution

It provides a novel connection between tachyon condensation, McKay correspondence, and D-branes as derived categories within the boundary string field theory framework.

Findings

Decay modes relate to McKay correspondence as complexes.

D-branes can be interpreted as objects in derived categories.

N=4 boundary supersymmetry offers a refined structural perspective.

Abstract

In this short note we present a mathematical interpretation of tachyon condensation on (three dimensional) orbifolds within the framework of boundary string field theory (BSFT). We explicitly show that important parts of decay modes in brane-antibrane systems with N=2 boundary supersymmetry can be interpreted as the McKay correspondence described as complexes. This will give an example of the recent interpretation of D-branes as derived category. We also discuss the N=4 boundary supersymmetry as a more refined structure.