Coulomb-gas formulation of SU(2) branes and chiral blocks

TL;DR

This paper develops a Coulomb-gas approach to construct and analyze boundary states in SU(2) WZNW models, providing explicit correlation functions and solutions to KZ equations, advancing understanding of D-branes in conformal field theory.

Contribution

It introduces a novel Coulomb-gas formulation for SU(2) branes and computes exact boundary correlation functions using this framework.

Findings

Constructed boundary states using bosonized Wakimoto representation.

Derived exact correlation functions for boundary primary fields.

Confirmed chiral blocks satisfy Knizhnik-Zamolodchikov equations.

Abstract

We construct boundary states in $SU(2)_k$ WZNW models using the bosonized Wakimoto free-field representation and study their properties. We introduce a Fock space representation of Ishibashi states which are coherent states of bosons with zero-mode momenta (boundary Coulomb-gas charges) summed over certain lattices according to Fock space resolution of $SU(2)_k$. The Virasoro invariance of the coherent states leads to families of boundary states including the B-type D-branes found by Maldacena, Moore and Seiberg, as well as the A-type corresponding to trivial current gluing conditions. We then use the Coulomb-gas technique to compute exact correlation functions of WZNW primary fields on the disk topology with A- and B-type Cardy states on the boundary. We check that the obtained chiral blocks for A-branes are solutions of the Knizhnik-Zamolodchikov equations.