Wrapped Magnetized Branes: Two Alternative Descriptions?

We discuss two inequivalent ways for describing magnetized D-branes wrapped N times on a torus T 2. The first one is based on a non-abelian gauge bundle U(N), while the second one is obtained by means of a Narain T-duality transformation acting on a theory with non-magnetized branes. We construct in both descriptions the boundary state and the open string vertices and show that they give rise to different string amplitudes. In particular, the description based on the gauge bundle has open string vertex operators with momentum dependent Chan-Paton factors. Work partially supported by the European Community’s Human Potential Programme under contract MRTN-CT-2004-005104 “Constituents, Fundamental Forces and Symmetries of the Universe” and by the Italian M.I.U.R. under contract PRIN-2005023102 “Strings, D-branes and Gauge Theories”. Three of us (PDV, RM, FP) thank the Galileo Galilei Institute for Theoretical Physics for their kind hospitality and for partial support during the completion of this work.