The Photon Dispersion as an Indicator for New Physics ?

TL;DR

This paper investigates potential deviations in photon dispersion relations as indicators of new physics, exploring non-commutative space theories and their implications for Lorentz invariance violation through numerical lattice studies.

Contribution

It provides a numerical analysis of pure U(1) gauge theory in non-commutative space, examining phase structure and implications for photon stability and Lorentz violation.

Findings

Photon dispersion deviations could signal new physics.

Non-commutative space leads to a phase with broken Poincare symmetry.

Photon remains IR stable despite IR divergence.

Abstract

We first comment on the search for a deviation from the linear photon dispersion relation, in particular based on cosmic photons from Gamma Ray Bursts. Then we consider the non-commutative space as a theoretical concept that could lead to such a deviation, which would be a manifestation of Lorentz Invariance Violation. In particular we review a numerical study of pure U(1) gauge theory in a 4d non-commutative space. Starting from a finite lattice, we explore the phase diagram and the extrapolation to the continuum and infinite volume. These simultaneous limits - taken at fixed non-commutativity - lead to a phase of broken Poincare symmetry, where the photon appears to be IR stable, despite a negative IR divergence to one loop.