Interfaces in the XY Model and Conformal Invariance

The one-dimensional XY model with n arbitrarily placed interfaces is investigated. The energy spectrum is shown to have a tower structure only for a commensurate configuration of the critical parameters. The interfacial critical exponents in such cases are determined from conformal invariance theory. The underlying algebra generating the conformal spectrum is the shifted SO(4c) Kac-Moody algebra, the central charge is 2c, which is exactly two times of that in the Ising model with the same structure of interfaces.