Factoring out free fields

TL;DR

This paper presents an algorithmic method for removing certain free fields from a generic  algebra, generalizing previous theorems and exploring the impact on induced gravity theories.

Contribution

It introduces a systematic procedure to factor out free fields of specific dimensions from  algebras, extending the Goddard-Schwimmer theorem.

Findings

Algorithm for factoring out free fields of dimension 1/2 and some of dimension 1.

Generalization of the Goddard-Schwimmer theorem for free fermions.

Relation between original and reduced  algebra induced gravity theories.

Abstract

For a generic $\Ww$ algebra, we give an algorithmic procedure for factoring out all fields of dimension $1/2$, both bosonic and fermionic, and some fields of dimension $1$. This generalizes and makes more explicit the Goddard-Schwimmer theorem for free fermions. We also show how the induced gravity theory for the original $\Ww$ algebra containing the free fields relates to the theory where the fields are factored out.