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We study relevant deformations of an N=1 superconformal theory which is an exactly marginal deformation of U(N) N=4 SUSY Yang-Mills. The resulting theory has a classical Higgs branch that is a complex deformation of the orbifold C^3/Z_n x…
The T-duality transformations between open and closed superstrings in different D-manifolds are generalized to curved backgrounds with commuting isometries. We address some global aspects like the occurrence of orientifold boundaries in…
We use mirror symmetry to establish the first concrete arena of spacetime topology change in string theory. In particular, we establish that the {\it quantum theories} based on certain nonlinear sigma models with topologically distinct…
We investigate the interrelation between topology and Narain T-duality of heterotic flux vacua. We present evidence that all 5 and 4-dimensional Minkowski space heterotic flux backgrounds with 8 supercharges have a locus in the moduli space…
Via T-duality a theory of open strings on a D1-brane wrapped along a cycle of slanted torus is described by a U(1) gauge theory on a D2-brane in the B-field background. It is also known that there is another dual description of the D1-brane…
We consider a class of super-conformal beta-deformed N=1 gauge theories dual to string theory on $AdS_5 \times X$ with fluxes, where $X$ is a deformed Sasaki-Einstein manifold. The supergravity backgrounds are explicit examples of…
T-duality acts on circle bundles by exchanging the first Chern class with the fiberwise integral of the H-flux, as we motivate using E_8 and also using S-duality. We present known and new examples including NS5-branes, nilmanifolds, Lens…
An overview is given of the construction of a differential polynomial ring of functions on the moduli space of Calabi-Yau threefolds. These rings coincide with the rings of quasi modular forms for geometries with duality groups for which…
A global analysis of duality transformations is presented. It is shown that duality between quantum field theories exists only when the geometrical structure of the quantum configuration spaces of the theories comply with certain precise…
In this paper we consider the quantization of open strings ending on D-branes with a background B field. We find that spacetime coordinates of the open string end-points become noncommutative, and correspondingly the D-brane worldvolume…
This is the second in a series of papers intended to set up a framework to study categories of modules in the context of non-commutative geometries. In \cite{mem} we introduced the basic DG category $\Pc_{\A^\bullet}$, the perfect category…
We show that the supermembrane theory compactified on a torus is invariant under T-duality. There are two different topological sectors of the compactified supermembrane (M2) classified according to a vanishing or nonvanishing second…
We study D=3 field theories on the D3-branes stretched between two NS5-branes with NS B-field background. The theory is a noncommutative gauge theory. The mirror symmetry and S-duality of the theory are discussed. A new feature is that the…
Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…
We investigate the D-brane contents of asymmetric orbifolds. Using T-duality we find that the consistent description of open strings in asymmetric orbifolds requires to turn on background gauge fields on the D-branes. We derive the…
We apply the $C^*$-algebraic formalism of topological T-duality due to Mathai and Rosenberg to a broad class of topological spaces that include the torus bundles appearing in string theory compactifications with duality twists, such as…
We study the quantum volume of D-branes wrapped around various cycles in Calabi-Yau manifolds, as the manifold's moduli are varied. In particular, we focus on the behaviour of these D-branes near phase transitions between distinct low…
With model building applications in mind, we collect and develop basic techniques to analyze the landscape of D7-branes in type IIB compact Calabi-Yau orientifolds, in three different pictures: F-theory, the D7 worldvolume theory and…
We define and study the moduli space of classical dynamical r-matrices associated to a Lie algebra g and a subalgebra l of g. As opposed to the previous papers q-alg/9703040 and q-alg/9706017 we do not make any commutativity assumption on…
We study the moduli spaces of heterotic/type II dual pairs in four dimensions with N=2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector…