We show that an essential assumption in the Vafa and Witten's theorem on P and CT realization in vector-like theories, the existence of a free energy density in Euclidean space in the presence of any external hermitian symmetry breaking source, does not apply if the symmetry is spontaneously broken. The assumption that the free energy density is well defined requires the previous assumption that the symmetry is realized in the vacuum. Even if Vafa and Witten's conjecture is plausible, actually a theorem is still lacking.

We propose a new approach to perform numerical simulations of theta-vacuum-like systems, test it in two analytically solvable models, and apply it to CP3. The main new ingredient in our approach is the method used to compute the probability distribution function of the topological charge at theta=0. We do not get unphysical phase transitions (flattening behavior of the free energy density) and reproduce the exact analytical results for the order parameter in the whole theta range within a few percent.

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Lattice formulation of Finite Baryon Density QCD is problematic from computer simulation point of view; it is well known that for light quark masses the reconstructed partition function fails to be positive in a wide region of parameter space. For large bare quark masses, instead, it is possible to obtain more sensible results; problems are still present but restricted to a small region. We present evidence for a saturation transition independent from the gauge coupling β and for a transition line that, starting from the temperature critical point at µ = 0, moves towards smaller β with increasing µ as expected from simplified phenomenological arguments.

The axion is one of the more interesting candidates to make the dark matter of the universe, and the axion potential plays a fundamental role in the determination of the dynamics of the axion field. Moreover, the way in which the U(1) A anomaly manifests itself in the chiral symmetry restored phase of QCD at high temperature could be tested when probing the QCD phase transition in relativistic heavy ion collisions. With these motivations, we investigate the physical consequences of the survival of the effects of the U(1) A anomaly in the chiral symmetric phase of QCD, and show that the free energy density is a singular function of the quark mass m, in the chiral limit, and that the σ and π susceptibilities diverge in this limit at any T ≥ T c. We also show that the difference between theπ andδ susceptibilities diverges in the chiral limit at any T ≥ T c , a result that can be contrasted with the existing lattice calculations; and discuss on the generalization of these results to the N f ≥ 3 model. ⋆ Acknowledges financial support by Ministerio de Economía y Competitividad under Grant No. FPA2015-65745-P (MINECO/FEDER).

We apply to the CP 9 model two recently proposed numerical techniques for the simulation of systems with a term. The algorithms, successfully tested in the strong coupling limit, are applied to the weak coupling region. The results agree and errors have been evaluated and are at the % level. The results scale well with the renormalization group equation and show that, for CP 9 in the presence of a term, CP symmetry is spontaneously broken at ϭ in the continuum limit.

We analyze the phase diagram of QCD with four staggered flavors in the (µ, T ) plane using a method recently proposed by us. We explore the region T 0.7 T C and µ 1.4 T C , where T C is the transition temperature at zero baryon density, and find a first order transition line. Our results are quantitatively compatible with those obtained with the imaginary chemical potential approach and the double reweighting method, in the region where these approaches are reliable, T 0.9T C and µ T C . But, in addition, our method allows us to extend the transition line to lower temperatures and higher chemical potentials. *

We propose a new method for the study of the chiral properties of the ground state in QFT's based on the computation of the probability distribution function of the chiral condensate. It can be applied directly in the chiral limit and therefore no mass extrapolations are needed. Furthermore this approach allows to write up equations relating the chiral condensate with quantities computable by standard numerical methods, the functional form of these relations depending on the broken symmetry group. As a check, we report some results for the compact Schwinger model.