On osp(2|2) conformal field theories

TL;DR

This paper develops free field realizations, screen currents, and primary fields for $osp(2|2)$ conformal field theories, providing new results that aid in supersymmetric approaches to disordered systems.

Contribution

It presents the first comprehensive construction of free field realizations and primary fields for $osp(2|2)^{(2)}_k$ and new insights for $osp(2|2)^{(1)}_k$.

Findings

Constructed free field realizations for $osp(2|2)$ superalgebras.

Derived screen currents and primary fields at general level $k$.

Provided new results relevant to supersymmetric disordered systems.

Abstract

We study the conformal field theories corresponding to current superalgebras $osp(2|2)^{(1)}_k$ and $osp(2|2)^{(2)}_k$. We construct the free field realizations, screen currents and primary fields of these current superalgebras at general level $k$. All the results for $osp(2|2)^{(2)}_k$ are new, and the results for the primary fields of $osp(2|2)^{(1)}_k$ also seem to be new. Our results are expected to be useful in the supersymmetric approach to Gaussian disordered systems such as random bond Ising model and Dirac model.