Free Field Realizations of Affine Current Superalgebras, Screening Currents and Primary Fields

TL;DR

This paper develops free field realizations for affine current superalgebras, including explicit constructions of currents, screening operators, and primary fields, facilitating the calculation of correlators in superalgebra models.

Contribution

It provides new, explicit free field realizations for affine superalgebras, extending previous work on affine algebras to the superalgebra case with general weights.

Findings

Explicit free field realizations of currents and primary fields

Construction of screening currents of the first kind

Framework for integral representations of correlators

Abstract

In this paper free field realizations of affine current superalgebras are considered. Based on quantizing differential operator realizations of the corresponding basic Lie superalgebras, general and simple expressions for both the bosonic and the fermionic currents are provided. Screening currents of the first kind are also presented. Finally, explicit free field realizations of primary fields with general, possibly non-integer, weights are worked out. A formalism is used where the (generally infinite) multiplet is replaced by a generating function primary operator. The results allow setting up integral representations for correlators of primary fields corresponding to integrable representations. The results are generalizations to superalgebras of a recent work on free field realizations of affine current algebras by Petersen, Yu and the present author.