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arXiv:hep-th/0611147 · Nuclear Physics B

On the SU(2|1) WZNW model and its statistical mechanics applications

Hubert Saleur, Volker Schomerus

Published Mar 22, 2007• 70 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2007.02.031

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Abstract We apply the recently developped analytical methods for computing the boundary entropy, or the g-function, in integrable theories with non-diagonal scattering. We consider the particular case of the current-perturbed SU (2) k WZNW model with boundary and compute the boundary entropy for a specific boundary condition. The main problem we encounter is that in case of non-diagonal scattering the boundary entropy is infinite. We show that this infinity can be cured by a subtraction. The difference of the boundary entropies in the UV and in the IR limits is finite, and matches the known g-functions for the unperturbed SU (2) k WZNW model for even values of the level.
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.