Open Strings and D-branes in WZNW model

TL;DR

The paper addresses open strings and D-branes in WZNW models under Poisson-Lie T-duality by developing a duality-invariant, topologically consistent framework. It introduces the triplet $(\Omega,\alpha_i,\alpha_f)$ to define the WZNW action for D-brane configurations via relative cohomology, derives the classical solvability and a nonlocal canonical map between dual brane phase spaces, and provides a practical method for evaluating interacting D-brane diagrams. A detailed SU($N$) WZNW example using a Drinfeld double illustrates brane geometry and confirms the absence of topological obstructions in the open-strip setup. Overall, the work unifies PL symmetry, D-brane geometry, and WZNW path integrals, yielding a rich structure of dual D-brane configurations in group manifolds and grounding quantum consistency through cohomological integrality 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.