Aspects of T-duality in Open Strings

TL;DR

The paper develops a canonical transformation framework to study T-duality for open strings in backgrounds with abelian and non-abelian isometries, focusing on explicit mappings between original and dual variables and the resulting boundary-condition transformations. It demonstrates that abelian duality maps Neumann to Dirichlet conditions, producing lower-dimensional D-branes, while non-abelian duality can yield curved D-branes in the dual (subject to quantum-equivalence conditions), with unoriented strings revealing curved orientifolds. The analysis extends to N=1 supersymmetric sigma models, identifying background constraints under which a dual super D-brane exists, and provides the supersymmetric non-abelian duality with curved D-branes. The work also discusses limitations, the need for a dilaton transformation, and open problems such as treating isotropic non-abelian backgrounds and connections to Poisson-Lie T-duality, offering a foundation for further exploration of curved-brane realizations under duality.

Abstract

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-abelian symmetry group. The generalization to $N=1$ supersymmetric sigma models with abelian and non-abelian isometries is also considered.