16 research outputs found
Conformal Toda theory with a boundary
We investigate sl(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>2) algebra. In one of
the two cases, we find that there exist D-branes 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
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>2) 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 B"acklund
transformation for sl(3) Toda classical mechanics, using the minisuperspace
limit of the bulk one-point function.Comment: 42 pages; version 4: added clarifications in section 2.2 and
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