Duality symmetries for strings moving in non-trivial spacetime backgrounds are analysed. It is shown that, for backgrounds generated from compact WZW and coset models, such duality symmetries are exact to all orders in string perturbation theory. A global treatment of duality symmetries is given, by associating them to the known symmetries of affine current algebras ( affine-Weyl group and exte...

The status of gaugino condensation in low-energy string theory is reviewed. Emphasis is given to the determination of the efective action below condensation scale in terms of the 2PI and Wilson actions. We illustrate how the different perturbative duality symmetries survive this simple nonperturbative phenomenon, providing evidence for the believe that these are exact nonperturbative symmetries...

We decompose tensor products of the defining representation of a Cartan type Lie algebra W (n) in the case where the number of tensoring does not exceed the rank of the Lie algebra. As a result, we get a kind of Schur duality between W (n) and a finite dimensional non-semisimple algebra, which is the semi-group ring of the transformation semigroup Tm .

This paper presents a uni ed study of duality properties for the problem of minimizing a linear function over the intersection of an a ne space with a convex cone in nite dimension. Existing duality results are carefully surveyed and some new duality properties are established. Examples are given to illustrate these new properties. The topics covered in this paper include Gordon-Stiemke type th...

The paper presents general machinery for extending a duality between complete, cocomplete categories to a duality between corresponding categories of semilattice representations (i.e. sheaves over Alexandrov spaces). This enables known dualities to be regularized. Among the applications, regularized Lindenbaun-Tarski duality shows that the weak extension of Boolean logic (i.e. the semantics of ...

A duality theorem for a pair of Wolfe-type second-order minimax mixed integer symmetric dual programs over cones is proved under separability and η-bonvexity/η-boncavity of the function k(x, y) appearing in the objective, where : . n m k R R R × ֏ Mond-Weir type symmetric duality over cones is also studied under η-pseudobonvexity/ηpseudoboncavity assumptions. Self duality (when the dual proble...