Coherent State Construction of Representations of osp(2|2) and Primary Fields of osp(2|2) Conformal Field Theory

TL;DR

This paper constructs all finite-dimensional representations of the superalgebra osp(2|2) and primary fields of the associated non-unitary conformal field theory using the vector coherent state method, for arbitrary level k.

Contribution

It provides a comprehensive construction of representations and primary fields of osp(2|2) and its affine extension in the standard basis, including both typical and atypical cases.

Findings

Constructed all finite-dimensional typical and atypical representations of osp(2|2).

Developed primary fields for osp(2|2)^{(1)}_k at arbitrary level k.

Applied the vector coherent state method to superalgebra representations.

Abstract

Representations of the superalgebra $osp(2|2)$ and current superalgebra $osp(2|2)^{(1)}_k$ in the standard basis are investigated. All finite-dimensional typical and atypical representations of $osp(2|2)$ are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with $osp(2|2)^{(1)}_k$ in the standard basis are constructed for arbitrary level $k$.