Journal of High Energy Physics

, 2010:89

Conformal Toda theory with a boundary

Open AccessArticle

DOI: 10.1007/JHEP12(2010)089

Cite this article as:
Fateev, V. & Ribault, S. J. High Energ. Phys. (2010) 2010: 89. doi:10.1007/JHEP12(2010)089


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 Wn≥3 algebra. In one of the two cases, we find that there exist D-branes of all possible dimensions 0 ≤ dn − 1, which correspond to partly degenerate representations of the Wn algebra. We perform classical and conformal bootstrap analyses of such D-branes, and relate these two approaches by using the semi-classical light asymptotic limit. In particular we determine the bulk one-point 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 Wn≥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 one-point function.


Integrable Equations in PhysicsD-branesConformal and W Symmetry
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Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique et Astroparticules, UMR5207 CNRS-UM2Montpellier Cedex 05France
  2. 2.Landau Institute for Theoretical PhysicsAcademy of Sciences of RussiaMoscowRussia