Spacetime foam, CPT anomaly, and photon propagation

TL;DR

This paper demonstrates that the CPT anomaly occurs in certain spacetime manifolds with arbitrarily small noncontractible loops, and proposes a model for photon propagation in a spacetime foam that modifies photon dispersion laws, constrained by gamma-ray observations.

Contribution

It extends the CPT anomaly to manifolds with arbitrarily small loops and introduces a photon propagation model in spacetime foam affecting dispersion laws.

Findings

CPT anomaly occurs in manifolds with small noncontractible loops.

Photon dispersion law is modified by spacetime foam structures.

Gamma-ray observations constrain the size of spacetime punctures.

Abstract

The CPT anomaly of certain chiral gauge theories has been established previously for flat multiply connected spacetime manifolds M of the type R^3 x S^1, where the noncontractible loops have a minimal length. In this article, we show that the CPT anomaly also occurs for manifolds where the noncontractible loops can be arbitrarily small. Our basic calculation is performed for a flat noncompact manifold with a single "puncture," namely M = R^2 x (R^2 {0}). A hypothetical spacetime foam might have many such punctures (or other structures with similar effects). Assuming the multiply connected structure of the foam to be time independent, we present a simple model for photon propagation, which generalizes the single-puncture result. This model leads to a modified dispersion law of the photon. Observations of high-energy photons (gamma-rays) from explosive extragalactic events can then be used to place an upper bound on the typical length scale of these punctures.