%0 Journal Article %T Exact C=1 Boundary Conformal Field Theories %A Curtis G. Callan %A Igor R. Klebanov %J Physics %D 1993 %I arXiv %R 10.1103/PhysRevLett.72.1968 %X We present a solution of the problem of a free massless scalar field on the half line interacting through a periodic potential on the boundary. For a critical value of the period, this system is a conformal field theory with a non-trivial and explicitly calculable S-matrix for scattering from the boundary. Unlike all other exactly solvable conformal field theories, it is non-rational ({\it i.e.} has infinitely many primary fields). It describes the critical behavior of a number of condensed matter systems, including dissipative quantum mechanics and of barriers in ``quantum wires''. %U http://arxiv.org/abs/hep-th/9311092v1