(Pseudo)Real Vacua

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.