Remarks on T-duality for open strings

TL;DR

The paper presents a sigma-model perspective on T-duality for open strings in the presence of abelian or non-abelian boundary gauge fields, using a functional-integral derivation that introduces an auxiliary boundary field to manage non-abelian Wilson loops and derives dual target-space data via Buscher-like transformations. It shows that the duality maps the bulk fields $(G,B)$ to $( ilde{G}, ilde{B})$ with explicit component relations and imposes Dirichlet boundary conditions on the dual coordinate, interpreting the dual as a D-brane with a matrix-valued boundary condition in the non-abelian case. The author then discusses the quantum aspects, pointing out that renormalization and Jacobians are essential for a rigorous equivalence beyond leading order, and that the relation between the gauge-field beta-functions on the D-brane and the Born-Infeld action is inhomogeneous, preventing a naive equivalence without further analysis. Overall, the work clarifies how T-duality operates for open strings with gauge fields and highlights subtleties in extending classical duality to the quantum regime on D-branes, with implications for D-brane dynamics and duality-consistent effective actions.

Abstract

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.