Spontaneous Parity Violation

TL;DR

This paper challenges the Vafa-Witten theorem by proposing a quantum fluctuation-driven mechanism for spontaneous parity violation, supported by a novel 5D meromorphic lattice formulation that alters the free energy landscape.

Contribution

It introduces a new lattice formulation and a mechanism that allows spontaneous parity breaking in vector-like gauge theories, contrary to previous beliefs.

Findings

Disproved the Vafa-Witten theorem.

Demonstrated a new lattice approach with a 5D meromorphic formulation.

Identified conditions where free energy minima differ from partition function maxima.

Abstract

We disprove the Vafa-Witten theorem on the impossibility of spontaneously breaking parity in vector-like gauge field theories, identifying a mechanism driven by quantum fluctuations. With the introduction of a meromorphic Lattice formulation, defined over 5 dimensions, we demonstrate that the minima of the free energy can be distinct from the maxima of the partition function : identifying and evaluating a suitable contour for the partition function defined such that asymptotic behaviour of the complex action is non-oscillatory.