An unsolved puzzle in quantum field theory is the absence or unexplained suppression of the otherwise legitimate presence in the theory of quantum chromodynamics (the strong force) of maximal violation of time reversal. In other words the movie of strong dynamics should run differently going forward and backward in time. The associated operator responsible for such a time violation is known as topological term. Because a good quantum theory respects Einstein’s special relativity (and locality) one can either speak of time violation or that the combined operation of charge conjugation and parity reversal (the physics in the mirror) is broken by the topological term but that the product CPT is preserved. 

The fascinating fact is that any resolution of the puzzle either requires new physical particles such as the axion and its siblings or new mechanisms in which time reversal is broken spontaneously or other exotic possibilities that indicate the presence of new physics. Experiments are now testing these ideas as you read this short article. 

Dealing with strong dynamics we must also face the technical challenge that it is hard to determine its physical consequences with pen and paper, and even super computers. Additionally, the situation becomes much more complicated if we wish to understand what happens when we squeeze strong matter very hard. This happens routinely in astrophysical objects such as neutron stars.

In our newly published work we investigate the sister theory of QCD, i.e. two-colour QCD at nonzero matter density and as function of the size of the time reversal breaking operator as well as the number of quarks. We show that the vacuum acquires a rich structure when the underlying CP violating 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 quark flavours. Our results will guide numerical simulations and novel tests of the model’s dynamics. The results are also expected to better inform phenomenological applications of the model ranging from composite Higgs physics to strongly interacting massive dark matter models featuring number changing interactions.