A note on the torsion dependence of D-brane RR couplings

The dependence on the torsion H = db of the Wess-Zumino couplings of Dbranes that are trivially embedded in space-time is studied. We show that even in this simple set-up some torsion components can be turned on, with a non-trivial effect on the RR couplings. In the special cases in which either the tangent or the normal bundle are trivial, the torsion dependence amounts to substitute the standard curvature with its generalization in the presence of torsion, in the usual couplings involving the roof genus Â. Since 1 October 2000: CERN, 1211 Geneva 23, Switzerland. E-mail: [email protected] Since 1 September 2000: ISAS-SISSA, Via Beirut 2-4, 34013 Trieste, Italy. E-mail: [email protected]