Deformed Kac-Moody Algebra and Noncommutative Fermi Theory in Two-Dimensions

TL;DR

This paper constructs a deformed Kac-Moody algebra for noncommutative two-dimensional Fermi theory, explicitly calculating higher-order corrections and showing that Schwinger terms remain unaffected by noncommutativity.

Contribution

It introduces a novel deformed Kac-Moody algebra framework for noncommutative Fermi theory, detailing higher-order corrections and their algebraic structure.

Findings

Schwinger terms are unaffected by noncommutativity.

Deformed algebra expressed as ordinary algebra plus infinite Lie structures.

Explicit calculations of higher-order corrections to the algebra.

Abstract

Starting from noncommutative Fermi theory in two-dimensions, we construct a deformed Kac-Moody algebra between its vector and Chiral currents . The higher-order corrections to the deformed Kac-Moody algebra are explicitly calculated. We observe that the ordinary Schwinger terms are not affected by noncommutativity. Finally we conclude that the deformed Kac-Moody algebra can be given in term of ordinary Kac-Moody algebra plus infinitely many Lie algebraic structures at each non-zero power of the antisymmetric coefficient $\theta$.