Spacetime foam,CPTanomaly, and photon propagation

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 × 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 × (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.

Photon-propagation model with random background field: Length scales and Cherenkov limits

“…VI of Ref. [1], where l γ was called l foam . This bound on l γ for A ∼ α is, in fact, of the order of the Planck length,…”

“…[1], specialized to the case l h = δ and with notations (l foam , d, a) for (l γ , l wormhole , l separation ) here, gave A = α in the effective action (7) and extra factors 0.18 and 0.15 on the right-hand sides of Eqs. (13a) and (13b), respectively.…”

“…We now turn to a simple photon-propagation model [1] with a fixed random background field g 1 (x) and an action given by…”

“…These definitions are motivated by a very simple spacetime model [1] consisting of static, randomly-distributed wormholes [6] embedded in Minkowski spacetime. This toy model has, by definition, a preferred frame of reference.…”

“…In a previous article [1], we have proposed a simple photon-propagation model to describe the potential effects of a static spacetime foam composed of identical, randomly-distributed defects (e.g., microscopic wormholes) embedded in Minkowski spacetime. For this particular model, a modified photon dispersion law was derived in the long-wavelength limit,…”