Conformal invariance and parastatistics in two dimensions

We show that the conformally invariant O(N) nonlinear σ-models with a Wess-Zumino term with coefficient k, have the same current and conformal algebras with a theory of N Majorana fermions with a hidden (gauged) O(k) quantum number. These latter are interpreted as N particles obeying the free Dirac equation but quantized with (nonlocal) para-Fermi statistics of order k, an interpretation that we verify by deriving the exact finite-temperature propagator, thereby explicitly relating the anomalous scaling dimensions to nonstandard statistics. (orig.)