, 2010:89,
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Date: 30 Dec 2010

Conformal Toda theory with a boundary

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 D-branes of all possible dimensions 0 ≤ dn − 1, which correspond to partly degenerate representations of the W n 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 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 one-point function.

ArXiv ePrint: 1007.1293