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

TL;DR

This paper examines the limitations of the Vafa-Witten theorem in finite-temperature QCD, showing it cannot exclude all forms of spontaneous parity violation, especially Lorentz-noninvariant operators.

Contribution

It demonstrates the inapplicability of the Vafa-Witten theorem to Lorentz-noninvariant parity-violating operators at finite temperature in QCD.

Findings

Vafa-Witten theorem rules out Lorentz-invariant parity violation

Lorentz-noninvariant parity-violating operators can acquire vacuum expectation values

The theorem's applicability is limited in certain finite-temperature QCD scenarios

Abstract

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.