Logarithmic Operators and Dynamical Extention of The Symmetry Group in the Bosonic SU(2)_0 and SUSY SU(2)_2 WZNW Models

TL;DR

The paper investigates operator product expansions in the bosonic SU(2)$_0$ and SUSY SU(2)$_2$ WZNW models, revealing logarithmic operators and new conserved currents that enlarge the symmetry algebra. By solving Knizhnik–Zamolodchikov equations and analyzing four-point functions, the authors identify logarithmic partners and construct an extended current algebra with currents $K^a$ and $N^a$, forming a Jordan-cell structure under $L_0$. In the SUSY case, a parallel analysis shows the theta-independent sector matches the bosonic theory and leads to a consistent identification of the additional currents within the superalgebra, yielding an $SO(4)_2$-type bosonic sector and compatible fermionic structure. The findings demonstrate dynamical symmetry extension in these critical WZNW models and suggest hidden symmetries with potential implications for disordered systems, polymers, strings, and related conformal field theories.

Abstract

We study the operator product expansion in the bosonic $SU(2)_0$ and SUSY $SU(2)_2$ WZNW models. We find that these OPEs contain both logarithmic operators and new conserved currents, leading to an extension of the symmetry group.