Integrable Four-Fermi Models with a Boundary and Boson-Fermion Duality

TL;DR

This paper extends integrable field theories to include fermionic models with boundaries, explores dualities between models, and identifies new boundary interactions in related theories.

Contribution

It introduces new boundary interactions for fermionic models and demonstrates dualities between different integrable models with boundaries.

Findings

Boundary interactions consistent with integrability are derived.

Duality between the massive Thirring and sine-Gordon models with boundaries is established.

New boundary interactions in the O(3) Gross-Neveu model are identified.

Abstract

Construction of integrable field theories in space with a boundary is extended to fermionic models. We obtain general forms of boundary interactions consistent with integrability of the massive Thirring model and study the duality equivalence of the MT model and the sine-Gordon model with boundary terms. We find a variety of integrable boundary interactions in the $O(3)$ Gross-Neveu model from the boundary supersymmetric sine-Gordon theory by using boson-fermion duality.