  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.
