Path Integral Bosonization of Massive GNO Fermions

TL;DR

This paper demonstrates the quantum equivalence between certain symmetric space sine-Gordon models and massive free fermions, providing a path integral bosonization framework for specific symmetric spaces and exploring their relation to nonabelian solitons.

Contribution

It introduces a path integral bosonization method for symmetric space sine-Gordon models, extending the GNO fermion framework to new symmetric spaces and analyzing their integrability and soliton relations.

Findings

Quantum equivalence between models established

Path integral bosonization formulated for specific symmetric spaces

Restrictions on fermion mass matrix linked to integrability

Abstract

We show the quantum equivalence between certain symmetric space sine-Gordon models and the massive free fermions. In the massless limit, these fermions reduce to the free fermions introduced by Goddard, Nahm and Olive (GNO) in association with symmetric spaces $K/G$. A path integral formulation is given in terms of the Wess-Zumino-Witten action where the field variable $g$ takes value in the orthogonal, unitary, and symplectic representations of the group $G$ in the basis of the symmetric space. We show that, for example, such a path integral bosonization is possible when the symmetric spaces $K/G$ are $SU(N) \times SU(N)/SU(N); N \le 3, ~ Sp(2)/U(2)$ or $SO(8)/U(4)$. We also address the relation between massive GNO fermions and the nonabelian solitons, and explain the restriction imposed on the fermion mass matrix due to the integrability of the bosonic model.