Comments on Two-Loop Kac-Moody Algebras

TL;DR

This paper demonstrates that two-loop Kac-Moody algebras can be represented as two-variable loop algebras plus free fields, revealing equivalences with certain conformal field theories and simplifying their structure.

Contribution

It establishes a novel equivalence between two-loop Kac-Moody algebras and simpler algebraic structures, facilitating analysis of related models.

Findings

Two-loop Kac-Moody algebra is equivalent to a two-variable loop algebra plus a decoupled system.

WZNW and CSW models with Kac-Moody symmetry are equivalent to multiple versions of standard models plus free fields.

The algebraic structure simplifies the understanding of models with two-loop Kac-Moody symmetry.

Abstract

It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and a decoupled $\beta$-$\gamma$ system. Similarly WZNW and CSW models having as algebraic structure the Kac-Moody algebra are equivalent to an infinity of versions of the corresponding ordinary models and decoupled abelian fields.