Comments On D-Brans On Orbifolds And K-Theory

We systematically revisit the description of D-branes on orbifolds and the classifi cation 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 Z(N) orbifolds with N odd are only BPS. We confirm this result using the boundary state formalism for Z(3). For Z(N) X Z(N) orbifolds with N odd, in the untwisted case and with discrete torsion whose class is a generator of H-3( Z/N X 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.