BPS bound states, supermembranes, and T-duality in M theory

This is an introductory review on the eleven-dimensional description of the BPS bound states of type II superstring theories, and on the role of supermembranes in M theory. The first part describes classical solutions of 11d supergravity which upon dimensional reduction and T-dualities give bound states of NS-NS and p-branes of type IIA and IIB string theories. In some cases (e.g. (q1,q2) string bound states of type IIB string theory), these non-perturbative objects admit a simple eleven-dimensional description in terms of a fundamental 2-brane. The BPS excitations of such 2-brane are calculated and shown to exactly match the mass spectrum for the BPS (q1,q2) string bound states. Different 11d representations of the same bound state can be used to provide inequivalent (T-dual) descriptions of the oscillating BPS states. This permits to test T-duality beyond perturbation theory and, in certain cases, to evade membrane instabilities by going to a stable T-dual representation. We finally summarize the results indicating in what regions of the modular parameter space a supermembrane description for M theory on R9 X T2 seems to be adequate. (Author). 49 refs., 2 figs