Vector-like symmetries and parity conservation in gauge theories with Yukawa couplings

TL;DR

This paper extends the positivity of the Euclidean path integral measure to certain gauge theories with Yukawa couplings, demonstrating parity conservation and deriving mass inequalities.

Contribution

It generalizes non-perturbative positivity results to parity-invariant theories with Yukawa couplings, establishing symmetry conservation and mass inequalities.

Findings

Positivity of the measure applies to theories with Dirac fermions and real gauge representations.

Parity and flavor symmetries are conserved in these theories.

Exact inequalities among hadron masses are derived.

Abstract

Non-perturbative results in QCD-like theories can be derived employing positivity of the Euclidean path integral measure, as pioneered by Weingarten, Vafa, Witten. We show that positivity of the measure can be generalized to parity-invariant theories with Yukawa couplings to fundamental scalars, provided the fermions are Dirac and carry a real representation of the gauge group. This result allows us to demonstrate the conservation of parity and vector-like flavor symmetries in such theories, as well as to derive exact inequalities among hadrons' masses.