Twisted Gauge Theories

TL;DR

This paper develops gauge theories on noncommutative space-time using twisting of the coproduct, leading to new gauge-invariant constructs and weakly coupled additional fields, with consistent equations and conservation laws.

Contribution

It introduces a novel method of constructing gauge theories on deformed space-time via twisting, resulting in new gauge-invariant quantities and weakly coupled additional fields.

Findings

Deformed Leibniz rule for gauge transformations.

Additional fields couple weakly via deformation parameter.

Consistent field equations with conservation laws.

Abstract

Gauge theories on a space-time that is deformed by the Moyal-Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is used to construct gauge invariant quantities. The connection will be enveloping algebra valued in a particular representation of the Lie algebra. This gives rise to additional fields, which couple only weakly via the deformation parameter and reduce in the commutative limit to free fields. Consistent field equations that lead to conservation laws are derived and some properties of such theories are discussed.