Spontaneous Lorentz Violation and Nonpolynomial Interactions

TL;DR

This paper explores how certain vector field theories with nonpolynomial interactions can lead to spontaneous Lorentz violation, potentially explaining photon behavior and suggesting new experimental tests.

Contribution

It demonstrates that nonpolynomial, gauge-noninvariant vector theories can be stable, relevant, and exhibit spontaneous Lorentz violation, with some theories being asymptotically free.

Findings

Spontaneous Lorentz violation occurs in these theories.

Nambu-Goldstone modes correspond to photons.

Identifies a class of asymptotically free theories.

Abstract

Gauge-noninvariant vector field theories with superficially nonrenormalizable nonpolynomial interactions are studied. We show that nontrivial relevant and stable theories have spontaneous Lorentz violation, and we present a large class of asymptotically free theories. The Nambu-Goldstone modes of these theories can be identified with the photon, with potential experimental implications.