T-duality for open strings

The purpose of this article is to present a pedagogical review of T-dualityin in string theory. The evolution of the closed string is envisaged on the worldsheet in the presence of its massless excitations. The duality symmetry is studied when some of the spacial coordinates are compactified on d-dimensional torus, $T^d$. The known results are reviewed to elucidate that equations of motion for the compact coordinates are $O(d,d)$ covariant, $d$ being the number of compact dir...

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 conditions. Applications to S-dual actions and to T duality of string theories and D-branes are briefly discussed.It is shown that a new topological term in the dual open string actions is required. We also study an extension of the procedure...

Nonrelativistic open string theory is defined by a worldsheet theory that produces a Galilean invariant string spectrum and is described at low energies by a nonrelativistic Yang-Mills theory. We study T-duality transformations in the path integral for the sigma model that describes nonrelativistic open string theory coupled to an arbitrary closed string background, described by a string Newton-Cartan geometry, Kalb-Ramond, and dilaton field. We prove that T-duality transform...

We discuss T-duality for open strings in general background fields both in the functional integral formulation as well as in the language of canonical transformations. The Dirichlet boundary condition in the dual theory has to be treated as a constraint on the functional integration. Furthermore, we give meaning to the notion of matrix valued string end point position in the presence of nonabelian gauge field background.

The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate string theory in T-fold backgrounds with T-duality transition functions and a quantum implementation of the constraints of the doubled formalism is presented. This establishes the quantum equivalence to the usual sigma-model formalism for wo...

Duality transformations with respect to rotational isometries relate supersymmetric with non-supersymmetric backgrounds in string theory. We find that non-local world-sheet effects have to be taken into account in order to restore supersymmetry at the string level. The underlying superconformal algebra remains the same, but in this case T-duality relates local with non-local realizations of the algebra in terms of parafermions. This is another example where stringy effects re...

In this article we review a recent calculation of the two-loop $\sigma$-model corrections to the T-duality map in string theory. Using the effective action approach, and focusing on backgrounds with a single Abelian isometry, we give the $O(\alpha')$ modifications of the lowest-order duality transformations. The torsion plays an important role in the theory to $O(\alpha')$, because of the Chern-Simons couplings to the gauge fields that arise via dimensional reduction.

We study T-duality for open strings on tori $\T^d$. The general boundary conditions for the open strings are constructed, and it is shown that T-duality group, which preserves the mass spectrum of closed strings, preserves also the mass spectrum of the open strings. The open strings are transformed to those with different boundary conditions by T-duality. We also discuss the T-duality for D-brane mass spectrum, and show that the D-branes and the open strings with both ends on...

We analyze in detail the possible breaking of spacetime supersymmetry under T-duality transformations. We find that when appropiate world-sheet effects are taken into account apparent puzzles concerning supersymmetry in spacetime are solved. We study T-duality in general heterotic $\sigma$-models analyzing possible anomalies, and we find some modifications of Buscher's rules. We then work out a simple but representative example which contains most of the difficulties. We also...

In this paper we study T-duality for open strings ending on branes with non-zero B-field on them from the point of view of canonical transformations. For the particular case of type II strings on the two torus we show that the $Sl(2,Z)_N$ transformations can be understood as a sub-class of canonical transformations on the open strings in the B-field background.