D-branes, discrete torsion and the McKay correspondence
We analyze the D-branes of a type-IIB string theory on an orbifold singularity including the possibility of discrete torsion following the work of Douglas et al. First we prove some general results about the moduli space of a point associated to the "regular representation" of the orbifold group. This includes some analysis of the "wrapped branes" which necessarily appear when the orbifold singularity is not isolated. Next we analyze the stringy homology of the orbifold using the McKay correspondence and the relationship between K-theory and homology. We find that discrete torsion and torsion in this stringy homology are closely-related concepts but that they differ in general. Lastly we question to what extent the D-1 brane may be thought of as being dual to a string.