The $\theta$-angle and axion physics of two-color QCD at fixed baryon charge. Part I

Understand

We analyze the impact of the $\theta$-angle and axion dynamics for two-color (in fact any $Sp(2N)$) QCD at nonzero baryon charge and as a function of the number of matter fields on the vacuum properties, the pattern of chiral symmetry breaking as well as the spectrum of the theory.

• We show that the vacuum acquires a rich structure when the underlying $CP$ violating topological operator is added to the theory.
• We discover novel phases and analyse the order of their transitions characterizing the dynamics of the odd and even number of flavours.
• We further determine the critical chemical potential as function of the $\theta$ angle separating the normal from the superfluid phase of the theory.