T duality for boundary-non-critical strings

Recent work on the action of T duality on Dirichlet-branes is generalized to the case in which the open string satisfies boundary conditions that are neither Neumann nor Dirichlet. This is achieved by implementing T duality as a canonical transformation of the $\sigma$-model path integral. A class of boundary interactions that violate conformal symmetry is found to be T-dual of a correspondingly non-conformal class of boundary conditions. The analogy with some problems in boundary-non-critical quantum mechanics of interest for condensed matter is pointed out.