Interfaces in the XY model and conformal invariance

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