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We study a strongly coupled $Z_2$ lattice gauge theory with two flavors ofquarks, invariant under an exact $\mathrm{SU}(2)\times \mathrm{SU}(2) \times\mathrm{U}_A(1) \times \mathrm{U}_B(1)$ symmetry which is the same as QCD withtwo flavors of quarks without an anomaly. The model also contains a couplingthat can be used to break the $\mathrm{U}_A(1)$ symmetry and thus mimic the QCDanomaly. At low temperatures $T$ and small baryon chemical potential $\mu_B$the model contains massless pions and massive bosonic baryons similar to QCDwith an even number of colors. In this work we study the $T-\mu_B$ phasediagram of the model and show that it contains three phases : (1) A chirallybroken phase at low $T$ and $\mu_B$, (2) a chirally symmetric baryon superfluidphase at low $T$ and high $\mu_B$, and (3) a symmetric phase at high $T$. Wefind that the nature of the finite temperature chiral phase transition and inparticular the location of the tricritical point that seperates the first orderline from the second order line is affected significantly by the anomaly.

Anomaly and a QCD-like phase diagram with massive bosonic baryons