Magnetic fields and fractional statistics in boundary conformal field theory

We study conformal field theories describing two massless one-dimensional fields interacting at a single spatial point. The interactions we include are periodic functions of the bosonized fields separately plus a "magnetic" interaction that mixes the two fields. Such models arise in open-string theory and dissipative quantum mechanics and perhaps in edge state tunneling in the fractional quantized Hall effect. The partition function for such theories is a Coulomb gas with interchange phases arising from the magnetic field. These "fractional statistics" have a profound effect on the phase structure of the Coulomb gas. In this paper we present new exact and approximate results for this type of generalized Coulomb gas.