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

TL;DR

This paper introduces a boundary WZNW model derived from the pairing Hamiltonian, modifying the Knizhnik-Zamolodchikov equations to include boundary effects, and connects correlators to the spectrum of the reduced pairing Hamiltonian.

Contribution

It constructs a deformed WZNW model with boundary terms by replacing Gaudin operators with pairing Hamiltonian constants of motion, linking correlation functions to the spectrum.

Findings

Correlators acquire exponential prefactors due to boundary effects.

The modified model satisfies deformed KZ equations involving the pairing Hamiltonian.

Establishes a connection between WZNW correlators and the spectrum of the reduced 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.