D-branes on orbifolds with discrete torsion and topological obstruction

Abstract

We find the orbifold analog of the topological relation recently found by Freed and Witten which restricts the allowed D-brane configurations of type-II vacua with a topologically non-trivial flat B-field. The result relies in Douglas proposal - which we derive from worldsheet consistency conditions - of embedding projective representations on open string Chan-Paton factors when considering orbifolds with discrete torsion. The orbifold action on open strings gives a natural definition of the algebraic K-theory group - using twisted cross products - responsible for measuring Ramond-Ramond charges in orbifolds with discrete torsion. We show that the correspondence between fractional branes and Ramond-Ramond fields follows in an interesting fashion from the way that discrete torsion is implemented on open and closed strings.