U–Duality Symmetries from the Membrane Worldvolume

We study U–duality symmetries of toroidally compactified M theory from the membrane worldvolume point of view. This is done taking the most general set of bosonic background fields into account. Upon restriction to pure moduli backgrounds, we are able to find the correct U–duality groups and moduli coset parameterizations for dimensions D > 6 as symmetries of the membrane worldvolume theory. In particular, we derive the D = 8 U–duality group SL(2)× SL(3). For general background fields, we concentrate on the caseD = 8. Though the SL(2) part of the symmetry appears to be obstructed by certain terms in the equations of motion, we are able to read off the transformation properties for the background fields. These transformations are verified by comparison with 11–dimensional supergravity dimensionally reduced to D = 8. ∗Supported by Deutsche Forschungsgemeinschaft (DFG) and Nato Collaborative Research Grant CRG. 940784.