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arXiv:hep-th/0403145 · Journal of Physics A Mathematical and General

Coulomb-gas formulation ofSU(2) branes and chiral blocks

Samuli Hemming, Shinsuke Kawai, Esko Keski-Vakkuri

Published Jun 8, 2005• 4 citations
arXivHTMLPDF

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.

DOI
10.1088/0305-4470/38/25/015

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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.
Starting with the SU ( 2 ) k WZW model, we construct boundary states that generically preserve only a parafermion times Virasoro subalgebra of the full affine Lie algebra symmetry of the bulk model. The boundary states come in families: intervals for generic k , quotients of SU ( 2 ) by discrete groups if k is a square. In that case, special members of the families can be viewed as superpositions of rotated Cardy branes. Using embeddings of SU ( 2 ) into higher groups, the new boundary states can be lifted to symmetry-breaking branes for other WZW models.
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Boundary Structure and Module Decomposition of the Bosonic Z2Z_2Z2​ Orbifold Models with R2=1/2kR^2=1/2kR2=1/2k
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