D-branes in orbifold singularities and equivariant K-theory

The study of brane-antibrane configurations in string theory leads to the understanding of supersymmetric Dp-branes as the bound states of higher dimensional branes. Configurations of pairs of brane-antibranes admit in a natural way a description in terms of K-theory. We analyze configurations of brane-antibranes 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-theoretical terms and their relation to the Kronheimer-Nakajima construction of instantons is also provided. Finally the D-brane charge formula is reexamined in this context. (C) 1999 Elsevier Science B.V. All rights reserved.