D-branes on Orbifolds with Discrete Torsion And Topological Obstruction

Details D-branes on Orbifolds with Discrete Torsion And Topological Obstruction D-branes on Orbifolds with Discrete Torsion And Topological Obstruction

2000-01-28

arxiv.org/abs/hep-th/0001200v2

JHEP 0005 (2000) 006

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, harvmac, clarification regarding relation with torsion in homology

Scientific paper

10.1088/1126-6708/2000/05/006

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.

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