D-branes in Orbifold Singularities and Equivariant K-Theory

TL;DR

This paper explores the classification of D-branes at orbifold singularities using equivariant K-theory, linking string theory configurations with advanced mathematical frameworks and reexamining D-brane charge formulas.

Contribution

It applies equivariant K-theory to analyze brane-antibrane configurations at orbifold singularities, connecting string theory with mathematical structures like Kronheimer-Nakajima instantons.

Findings

K-theoretic description of brane-antibrane at orbifold singularities

Relation between D-branes and Kronheimer-Nakajima instantons

Reevaluation of D-brane charge formulas in this context

Abstract

The study of brane-antibrane configurations in string theory leads to the understanding of supersymmetric D$p$-branes as the bound states of higher dimensional branes. Configurations of pairs brane-antibrane do admit in a natural way their description in terms of K-theory. We analyze configurations of brane-antibrane at fixed point orbifold singularities in terms of equivariant K-theory as recently suggested by Witten. Type I and IIB fivebranes and small instantons on ALE singularities are described in K-theoretic terms and their relation to Kronheimer-Nakajima construction of instantons is also provided. Finally the D-brane charge formula is reexamined in this context.