(Pseudo)Real Vacua

TL;DR

This paper investigates how the vacuum state in fermionic gauge theories with real or pseudoreal representations changes discontinuously at certain fermion mass values, revealing multiple vacua linked to symmetry properties.

Contribution

It identifies critical points where the vacuum jumps in theories with real or pseudoreal fermion representations, highlighting differences from complex representation cases.

Findings

Discontinuous vacuum transitions at zero fermion mass

Existence of four distinct vacua based on mass sign

Enhanced symmetry prevents CP violation at specific points

Abstract

We study the alignment of the vacuum in fermionic gauge theories with enhanced global symmetries by adding a small explicit mass term. Specifically we center our investigations around the theories with two Dirac fermions in a real or pseudoreal representation of the gauge group. We find that as we vary the explicit fermion masses $m_U$ and $m_D$ there are critical points where the system makes a discontinuous jump from one vacuum to another. This occurs when one of the fermion masses vanish. Hence there are four unique vacua depending only on the sign of $m_U$ and $m_D$. Due to the enhanced global symmetry nothing is therefore expected to happen at the point $m_U=-m_D$ where, on the other hand, theories with fermions in a complex representation of the gauge group are expected to develop a CP violating (Dashen) phase.