Free field realization of the exceptional current superalgebra $\hat{D(2,1;\a)}_k$

TL;DR

This paper constructs free-field representations and screening currents for the exceptional current superalgebra D(2,1;α), providing tools for studying its structure and applications in conformal field theory.

Contribution

It introduces explicit free-field realizations and screening currents for the D(2,1;α) superalgebra, advancing the understanding of its algebraic structure.

Findings

Constructed free-field representations of D(2,1;α)

Derived the energy-momentum tensor for the superalgebra

Presented screening currents of the first kind

Abstract

The free-field representations of the $D(2,1;\a)$ current superalgebra and the corresponding energy-momentum tensor are constructed. The related screening currents of the first kind are also presented.