T-duality for open strings

We study T-duality for open strings in various $D$-manifolds in the approach of canonical transformations. We show that this approach is particularly useful to study the mapping of the boundary conditions since it provides an explicit relation between initial and dual variables. We consider non-abelian duality transformations and show that under some restrictions the dual is a curved $(d-{\rm dim}G-1)$ D-brane, where $d$ is the dimension of the space-time and $G$ the non-abel...

In the first part of the talk we discuss T-duality for a free boson on a world sheet with boundary in a setting suitable for the generalization to non-trivial backgrounds. The gauging method as well as the canonical transformation are considered. In both cases Dirichlet strings as T-duals of Neumann strings arise in a generic way. In the second part the gauging method is employed to construct the T-dual of a model with non-Abelian isometries.

Recent work on the action of T duality on Dirichlet-branes is generalized to the case in which the open string satisfies boundary conditions that are neither Neumann nor Dirichlet. This is achieved by implementing T duality as a canonical transformation of the $\sigma$-model path integral. A class of boundary interactions that violate conformal symmetry is found to be T-dual of a correspondingly non-conformal class of boundary conditions. The analogy with some problems in bou...

This contribution gives in sigma-model language a short review of recent work on T-duality for open strings in the presence of abelian or non-abelian gauge fields. Furthermore, it adds a critical discussion of the relation between RG beta-functions and the Born-Infeld action in the case of a string coupled to a D-brane.

A manifestly T-dual invariant formulation of bosonic string theory is discussed here. It can be obtained by making both the usual string compact coordinates and their duals explicitly appear, on the same footing, in the world-sheet action. A peculiarity of such a model is the loss of the local Lorentz invariance which is required to be recovered on-shell. This dictates a constraint on the backgrounds which characterizes the double geometry of the target space. Constant and no...

We revisit T-duality transformations for the open string via Buscher's procedure and work-out technical details which have been missing so far in the literature. We take into account non-trivial topologies of the world-sheet, we consider T-duality along directions with Neumann as well as Dirichlet boundary conditions, and we include collective T-duality along multiple directions. We illustrate this formalism with the example of the three-torus with H-flux and its T-dual bac...

The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to T-duality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fib...

We present a brief review on the canonical transformation description of some duality symmetries in string and gauge theories. In particular, we consider abelian and non-abelian T-dualities in closed and open string theories as well as S-duality in abelian and non-abelian non-supersymmetric gauge theories.

We gauge the non-abelian isometries of a sigma model with boundaries. Forcing the field strength of the gauge fields to vanish renders the gauged model equivalent to the ungauged one provided that boundary conditions are taken into account properly. Integrating out the gauge fields gives the T-dual model. We observe that T-duality interchanges Neumann (or mixed) boundary conditions with Dirichlet boundary conditions.

We study non-local realizations of extended worldsheet supersymmetries and the associated space-time supersymmetries which arise under a T-duality transformation. These non-local effects appear when the supersymmetries do not commute with the isometry with respect to which T-duality is performed.