Conformal Toda theory with a boundary
 Vladimir Fateev,
 Sylvain Ribault
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Abstract
We investigate \( s{\ell_n} \) conformal Toda theory with maximally symmetric boundaries. There are two types of maximally symmetric boundary conditions, due to the existence of an order two automorphism of the W _{ n≥3} algebra. In one of the two cases, we find that there exist Dbranes of all possible dimensions 0 ≤ d ≤ n − 1, which correspond to partly degenerate representations of the W _{ n } algebra. We perform classical and conformal bootstrap analyses of such Dbranes, and relate these two approaches by using the semiclassical light asymptotic limit. In particular we determine the bulk onepoint functions. We observe remarkably severe divergences in the annulus partition functions, and attribute their origin to the existence of infinite multiplicities in the fusion of representations of the W _{ n≥3} algebra. We also comment on the issue of the existence of a boundary action, using the calculus of constrained functional forms, and derive the generating function of the Bäcklund transformation for \( s{\ell_3} \) Toda classical mechanics, using the minisuperspace limit of the bulk onepoint function.
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 Title
 Conformal Toda theory with a boundary
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Journal of High Energy Physics
2010:89
 Online Date
 December 2010
 DOI
 10.1007/JHEP12(2010)089
 Online ISSN
 10298479
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Integrable Equations in Physics
 Dbranes
 Conformal and W Symmetry
 Industry Sectors
 Authors

 Vladimir Fateev ^{(1)} ^{(2)}
 Sylvain Ribault ^{(1)}
 Author Affiliations

 1. Laboratoire de Physique Théorique et Astroparticules, UMR5207 CNRSUM2, Université Montpellier II, Place E. Bataillon, 34095, Montpellier Cedex 05, France
 2. Landau Institute for Theoretical Physics, Academy of Sciences of Russia, Kosygina Str. 2, 117334, Moscow, Russia