Open Strings and D-branes in WZNW model

TL;DR

This paper explores the rich structure of D-branes in WZNW models, revealing Poisson-Lie symmetries and dualities that define their configurations and path integral formulations.

Contribution

It uncovers Poisson-Lie symmetries in WZNW models and details their role in dual D-brane configurations, including conditions for well-defined path integrals.

Findings

Poisson-Lie symmetries in WZNW models

Dual pairs of D-branes characterized by shapes and two-forms

Path integral unambiguously defined under cocycle conditions

Abstract

An abundance of the Poisson-Lie symmetries of the WZNW models is uncovered. They give rise, via the Poisson-Lie $T$-duality, to a rich structure of the dual pairs of $D$-branes configurations in group manifolds. The $D$-branes are characterized by their shapes and certain two-forms living on them. The WZNW path integral for the interacting $D$-branes diagrams is unambiguously defined if the two-form on the $D$-brane and the WZNW three-form on the group form an integer-valued cocycle in the relative singular cohomology of the group manifold with respect to its $D$-brane submanifold. An example of the $SU(N)$ WZNW model is studied in some detail.