Worldsheet boundary conditions in Poisson-Lie T-duality

TL;DR

This paper demonstrates that bosonic open string boundary conditions are invariant under Poisson-Lie T-duality at the classical level, ensuring the dual model remains conformal and providing a duality map for D-brane boundary conditions.

Contribution

It introduces a method to apply Poisson-Lie T-duality to open string boundary conditions, preserving conformal invariance and deriving a duality map for D-branes in non-Abelian Drinfel'd doubles.

Findings

Boundary conditions are invariant under Poisson-Lie T-duality.

Conformal invariance of boundary conditions is preserved.

Explicit duality map for D-branes in non-Abelian doubles.

Abstract

We apply canonical Poisson-Lie T-duality transformations to bosonic open string worldsheet boundary conditions, showing that the form of these conditions is invariant at the classical level, and therefore they are compatible with Poisson-Lie T-duality. In particular the conditions for conformal invariance are automatically preserved, rendering also the dual model conformal. The boundary conditions are defined in terms of a gluing matrix which encodes the properties of D-branes, and we derive the duality map for this matrix. We demonstrate explicitly the implications of this map for D-branes in two non-Abelian Drinfel'd doubles.