Spacetime foam,CPTanomaly, and photon propagation

The CPT anomaly of certain chiral gauge theories has been established previously for flat multiply connected spacetime manifolds M of the type $R^3\times S^1,$ 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 $M=R^2\times \left(R^2\backslash \{0\}\right).\mathrm{}$ 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.