Description of D-branes invariant under the Poisson-Lie T-plurality

TL;DR

This paper characterizes D-branes in open string theory using gluing matrices, demonstrating their invariance under Poisson-Lie T-plurality transformations through geometric conditions related to the Drinfel'd double.

Contribution

It establishes a geometric criterion for D-branes' invariance under Poisson-Lie T-plurality by linking gluing matrices to right cosets in the Drinfel'd double.

Findings

Gluing matrices encode D-brane boundary conditions.

Invariance under Poisson-Lie T-plurality is shown via Drinfel'd double cosets.

Constraints on gluing matrices are equivalent to geometric invariance.

Abstract

We write the conditions for open strings with charged endpoints in the language of gluing matrices. We identify constraints imposed on the gluing matrices that are essential in this setup and investigate the question of their invariance under the Poisson-Lie T-plurality transformations. We show that the chosen set of constraints is equivalent to the statement that the lifts of D-branes into the Drinfel'd double are right cosets with respect to a maximally isotropic subgroup and therefore it is invariant under the Poisson-Lie T-plurality transformations.