Boundary Wess-Zumino-Novikov-Witten Model from the Pairing Hamiltonian

Abstract: Correlation functions of primary fields in the Wess-Zumino-Novikov-Witten (WZNW) model are known to satisfy a system of Knizhnik-Zamolodchikov (KZ) equations, which involve constants of motion of the exactly-solvable Gaudin magnet. We modify the KZ equations by replacing these Gaudin operators with constants of motion of the closely-related Richardson pairing Hamiltonian and reconstruct a deformed WZNW model, whose correlators satisfy these equations. This modified theory, dubbed here the boundary WZNW model, contains a term that breaks translational symmetry and therefore represents a generalized boundary operator. The corresponding correlators of the boundary WZNW model are calculated and are shown to acquire exponential prefactors, in contrast to the bulk WZNW theories. The solution also establishes a connection between correlation functions of the WZNW model and the spectrum of the reduced pairing Hamiltonian.