Abstract
The relation between parafermion field theories of order Q and the corresponding fermion field theories with SO(Q) symmetry is studied. It is shown that these theories are related but not identical. The explicit relation between the states and the observables of the two classes of theories are given without using the Klein transformations. The formalism is applied to the free conformally invariant parafermion theories in two dimensions. Their Virasoro algebra and SO(N) Kac–Moody algebra are given. The equivalence of their canonical form of the energy-momentum tensor with the Sugawara–Sommerfield form is also elucidated.
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