Tachyon condensation on orbifolds and McKay correspondence

In this Letter 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.