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Non-perturbative states in type II superstring theory from classical spinning membranes

We find a new family of exact solutions in membrane theory, representing toroidal membranes spinning in several planes. They have energy square proportional to the sum of the different angular momenta, generalizing Regge-type string solutions to membrane theory. By compactifying the eleven dimensional theory on a circle and on a torus, we identify a family of new non-perturbative states of type IIA and type IIB superstring theory (which contains the perturbative spinning string solutions of type II string theory as a particular case). The solution represents a spinning bound state of D branes and fundamental strings. Then we find similar solutions for membranes on $AdS_7\times S^4$ and $AdS_4\times S^7$. We also consider the analogous solutions in SU(N) matrix theory, and compute the energy. They can be interpreted as rotating open strings with D0 branes attached to their endpoints.