D-branes in orbifold singularities and equivariant K-theory

The study of brane-antibrane configurations in string theory leads to the u nderstanding of supersymmetric Dp-branes as the bound states of higher dime nsional branes. Configurations of pairs of brane-antibranes admit in a natu ral way a description in terms of K-theory. We analyze configurations of br ane-antibranes at fixed point orbifold singularities in terms of equivarian t K-theory as recently suggested by Witten. Type I and IIB fivebranes and s mall instantons on ALE singularities are described in K-theoretical terms a nd their relation to the Kronheimer-Nakajima construction of instantons is also provided. Finally the D-brane charge formula is reexamined in this con text. (C) 1999 Elsevier Science B.V. All rights reserved.