Second order expansions of action functionals of noncommutative gauge theories

TL;DR

This paper derives second order expansions of gauge action functionals on noncommutative spaces, discusses ambiguities in the expansion, and explores implications for noncommutative gauge theories as potential extensions of the Standard Model.

Contribution

It provides explicit second order expansions of noncommutative gauge actions and analyzes the ambiguities affecting these expansions.

Findings

Second order expanded gauge actions are derived.

Ambiguities in the expansion are identified and discussed.

Implications for noncommutative gauge theories as Standard Model extensions are considered.

Abstract

Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus be a serious candidate for an extension of the Standard Model. This note contains the results for expanded gauge theory actions on a noncommutative space with constant theta, up to second order, together with a discussion of the ambiguities of the expanded theory and how they affect the action.