Spontaneous Parity Violation in QCD At Finite Temperature: On the Inapplicability of the Vafa-Witten Theorem

The generalization of the Vafa-Witten theorem ruling out parity violation to QCD at finite temperature is considered. It is shown that this generalization of the theorem rules out Lorentz-invariant parity violating operators from spontaneously acquiring vacuum expectation values. However, it does not rule out Lorentz-noninvariant parity-violating operators from acquiring expectation values. Other situations where the theorem is inapplicable are also discussed.