Conformal Toda theory with a boundary

Understand

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.