Comments on D-branes on orbifolds and K-theory

Abstract

We systematically revisit the description of D-branes on orbifolds and the classification of their charges via K-theory. We include enough details to make the results accessible to both physicists and mathematicians interested in these topics. The minimally charged branes predicted by K-theory in ℤN orbifolds with N odd are only BPS. We confirm this result using the boundary state formalism for ℤ3. For ℤN × ℤN orbifolds with N odd, in the untwisted case and with discrete torsion whose class is a generator of H3(ℤ/N × ℤ/N,ℤ), we show that the K-theory classification of charges agrees with the boundary state approach, largely developed by Gaberdiel and collaborators, including the types of representation on the Chan–Paton factors.