Integrable quantum field theories with supergroup symmetries: the $OSP(1/2)$ case

TL;DR

This paper explores integrable 1+1 dimensional quantum field theories with supergroup symmetries, focusing on the $OSP(1/2)$ case, and provides new models, solutions, and lattice realizations, including the first physical realization of a super WZW model.

Contribution

It introduces new integrable models with supergroup symmetry, solves their generalizations, and offers the first physical lattice realization of a super WZW model.

Findings

Solutions for generalized models with supergroup symmetry.

Identification of a new class of models with non-linear symmetry realization.

Integrable lattice models that flow to super WZW models.

Abstract

As a step to understand general patterns of integrability in 1+1 quantum field theories with supergroup symmetry, we study in details the case of $OSP(1/2)$. Our results include the solutions of natural generalizations of models with ordinary group symmetry: the $UOSP(1/2)_{k}$ WZW model with a current current perturbation, the $UOSP(1/2)$ principal chiral model, and the $UOSP(1/2)\otimes UOSP(1/2)/UOSP(1/2)$ coset models perturbed by the adjoint. Graded parafermions are also discussed. A pattern peculiar to supergroups is the emergence of another class of models, whose simplest representative is the $OSP(1/2)/OSP(0/2)$ sigma model, where the (non unitary) orthosymplectic symmetry is realized non linearly (and can be spontaneously broken). For most models, we provide an integrable lattice realization. We show in particular that integrable $osp(1/2)$ spin chains with integer spin flow to $UOSP(1/2)$ WZW models in the continuum limit, hence providing what is to our knowledge the first physical realization of a super WZW model.