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A brief review of the status of duality symmetries in string theory is presented. The evidence is accumulating rapidly that an enormous group of duality symmetries, including perturbative T dualities and non-perturbative S-dualities,…

The partition function of type IIA and B strings on R^6xK3, in the T^4/Z_2 orbifold limit, is explicitly computed as a modular invariant sum over spin strutures required by perturbative unitarity in order to extend the analysis to include…

In this lecture we review some of the recent developments in string theory on an introductory and qualitative level. In particular we focus on S-T-U dualities of toroidally compactified ten-dimensional string theories and outline the…

Inspired by the low wave-length limit of topological M-theory, which re-constructs the theory of $3+1$D gravity in the self-dual variables' formulation, and by the realization that in Loop Quantum Gravity the holonomy of a flat connection…

T-Duality is a poorly understood symmetry of the space-time fields of string theory that interchanges long and short distances. It is best understood in the context of toroidal compactification where, loosely speaking, radii of the torus…

We state and prove a general result establishing that T-duality simplifies the bulk-boundary correspondence, in the sense of converting it to a simple geometric restriction map. This settles in the affirmative several earlier conjectures of…

The strong coupling limit of a quantum system is in general quite complicated, but in some cases a great simplification occurs: the strongly coupled limit is equivalent to the weakly coupled limit of some other system. In string theory…

One of the dualities in string theory, the F-theory/heterotic string duality in eight dimensions, predicts an interesting correspondence between two seemingly disparate geometrical objects. On one side of the duality there are elliptically…

This is a very brief survey of some results in the geometry of string duality delivered at a lecture given at ICM 1998, Berlin. String Duality is the statement that one kind of string theory compactified on one space is equivalent in some…

We address the issue of T-duality and U-duality symmetries in the toroidally-compactified type IIA string. It is customary to take as a starting point the dimensionally-reduced maximal supergravity theories, with certain field strengths…

We revisit the fundamental string (F1) solution in the doubled formalism. We show that the wave-like solution of double field theory (DFT) corresponding to the F1/pp-wave duality pair is more properly a solution of the DFT action coupled to…

In this paper, we establish graded T-duality for $2d$ $\sigma$-models with $H$-flux after localization. This establishes the most general version of T-duality for Type II String Theory. The graded T-duality map, which we call {\bf graded…

Timelike T-duality of string theory appears as a symmetry of time evolution in string field theory, exchanging evolution through times t and 1/t, and exchanging boundary states with backgrounds. This is demonstrated by constructing the…

We extend the $C^{\ast}-$algebraic formalism of Topological T-duality to section algebras of locally trivial bundles of strongly self-absorbing $C^{\ast}-$algebras and to a larger class of String Theoretic dualities. We argue that…

We examine T-duality transformations for supersymmetric strings with target space geometry with compact abelian isometries. We consider the partition function of these models and we show that although T-duality is not a symmetry, due to an…

We discuss a T-duality transformation for the c=1/2 matrix model for the purpose of studying duality transformations in a possible toy example of nonperturbative frameworks of string theory. Our approach is to first investigate the scaling…

Double Field Theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical…

This presentation is intended to give a flavour of the physics to be studied and discovered by exploiting the interface between string theory, M-theory and field theory provided by the dynamics of extended objects called `branes', and their…

We clarify the relation between various approaches to the manifestly T-duality symmetric string. We explain in detail how the PST covariant doubled string arises from an unusual gauge fixing. We pay careful attention to the role of…

String backgrounds with a local torus fibration such as T-folds are naturally formulated in a doubled formalism in which the torus fibres are doubled to include dual coordinates conjugate to winding number. Here we formulate and explore a…