U-duality and M-theory, an algebraic approach
Based on our work , we discuss how U-duality arises as an exact symmetry of M-theory from T-duality and 11D diffeomorphism invariance. A set of Weyl generators are shown to realize the Weyl group of SO(d, d, Z) and E d(d) , while Borel generators extend these finite groups into the full T- and U-duality groups. We discuss how the BPS states fall into various representations, and obtain duality invariant mass formulae, relevant for the computation of exact string amplitudes. The realization of U-duality symmetry in Matrix gauge theory is also considered.
KeywordsGauge Theory Modulus Space Weyl Group Mapping Class Group Dehn Twist
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