SU(2)_0 and OSp(2|2)_{-2} WZNW models : Two current algebras, one Logarithmic CFT

TL;DR

This paper reveals a hidden OSp(2|2)_{-2} symmetry in the SU(2)_0 WZNW model, linking its logarithmic correlation functions to a c=-2 sector and exploring boundary effects.

Contribution

It uncovers the hidden OSp(2|2)_{-2} symmetry in SU(2)_0 and connects its logarithmic structure to the c=-2 sector, providing new insights into boundary phenomena.

Findings

SU(2)_0 has a hidden OSp(2|2)_{-2} symmetry.

Logarithmic correlations originate from the c=-2 sector.

Quantum Hamiltonian reduction relates SU(2)_0 to the c=-2 model.

Abstract

We show that the SU(2)_0 WZNW model has a hidden OSp(2|2)_{-2} symmetry. Both these theories are known to have logarithms in their correlation functions. We also show that, like OSp(2|2)_{-2}, the logarithmic structure present in the SU(2)_0 model is due to the underlying c=-2 sector. We also demonstrate that the quantum Hamiltonian reduction of SU(2)_0 leads very directly to the correlation functions of the c=-2 model. We also discuss some of the novel boundary effects which can take place in this model.