Asymptotically Free Lorentz- and CPT-Violating Scalar Field Theories

TL;DR

This paper introduces a new class of Lorentz- and CPT-violating scalar field theories with nonpolynomial interactions, many of which are asymptotically free and stable under certain conditions, expanding the landscape of possible fundamental theories.

Contribution

It discovers nonpolynomial Lorentz- and CPT-violating scalar field theories that are asymptotically free, beyond the standard model extension.

Findings

Identifies nonpolynomial scalar interactions involving high powers of the field.

Many of these interactions form asymptotically free theories.

Theories are stable if rotation invariance remains unbroken.

Abstract

We search for novel Lorentz- and CPT-violating field theories, beyond those contained in the superficially renormalizable standard model extension. We find a new class of scalar field self-interactions which are nonpolynomial in form, involving arbitrarily high powers of the field. Many of these interactions correspond to nontrivial asymptotically free theories. These theories are stable if rotation invariance remains unbroken. These results indicate that certain forms of Lorentz violation, if they exist, may naturally be quite strong.