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

Samuli Hemming·Shinsuke Kawai·Esko Keski-Vakkuri
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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.

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Samuli Hemming, Shinsuke Kawai, Esko Keski-Vakkuri. 2005-05-21. Coulomb-gas formulation of SU(2) branes and chiral blocks. https://doi.org/10.1088/0305-4470%2F38%2F25%2F015

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