Conformal field theory and the exact solution of the BCS Hamiltonian

We propose a connection between conformal field theory (CFT) and the exact solution and integrability of the reduced BCS model of superconductivity. T he relevant CFT is given by the SU(2)(k)-WZW model in the singular limit wh en the level k goes to -2. This theory has to be perturbed by an operator p roportional to the inverse of the BCS coupling constant. Using the free fie ld realization of this perturbed Wess-Zumino-Witten model, we derive the ex act Richardson's wave function and the integrals of motion of the reduced B CS model in the saddle point approximation. The construction is reminiscent of the CFT approach to the Fractional Quantum Hall effect. (C) 2000 Elsevi er Science B.V. All rights reserved.