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Conformal Field Theory and the Exact Solution of the BCS Hamiltonian
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abstract
We propose a connection between conformal field theory (CFT) and the exact solution and integrability of the reduced BCS model of superconductivity. The relevant CFT is given by the $SU(2)_k$-WZW model in the singular limit when the level k goes to -2. This theory has to be perturbed by an operator proportional to the inverse of the BCS coupling constant. Using the free field realization of this perturbed Wess-Zumino-Witten model, we derive the exact Richardson's wave function and the integrals of motion of the reduced BCS model in the saddle point approximation. The construction is reminiscent of the CFT approach to the Fractional Quantum Hall effect.
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Cited by 1 Pith paper
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2D CFT and efficient Bethe ansatz for exactly solvable Richardson-Gaudin models
The paper identifies the Richardson Yang-Yang function with a Gaiotto-Witten irregular Virasoro block and provides a numerical solver for the Bethe equations of Richardson-Gaudin models.
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