Lattice simulations with analytic continuation suggest that SU(2) Yang-Mills has a deconfined phase with spontaneously broken CP symmetry at theta=pi.
Behavior near $\theta=\pi$ of the mass gap in the 2D O(3) non-linear sigma model
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The validity of the Haldane's conjecture entails that the mass gap of the 2-dimensional O(3) non-linear sigma model with a $\theta$-term must tend to zero as $\theta$ approaches the value $\pi$ by following a precise law. In the present paper we extract the related critical exponents by simulating the model at imaginary $\theta$.
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Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations
Lattice simulations with analytic continuation suggest that SU(2) Yang-Mills has a deconfined phase with spontaneously broken CP symmetry at theta=pi.