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.

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.

In breast cancer it has been proposed that the presence of cancer stem cells may drive tumor initiation, progression and recurrences. IL-8, up-regulated in breast cancer, and associated with poor prognosis, increases CSC self-renewal in cell line models. It signals via two cell surface receptors, CXCR1 and CXCR2. Recently, the IL-8/CXCR1 axis was proposed as an attractive pathway for the design of specific therapies against breast cancer stem cells. Reparixin, a powerful CXCR1 inhibitor, was effective in reducing in vivo the tumour-initiating population in several NOD/SCID mice breast cancer models, showing that the selective targeting of CXCR1 and the combination of reparixin and docetaxel resulted in a concomitant reduction of the bulk tumour mass and CSC population. The available data indicate that IL-8, expressed by tumour cells and induced by chemotherapeutic treatment, is a key regulator of the survival and self-renewal of the population of CXCR1-expressing CSC. Consequently, this investigation on the mechanism of action of the reparixin/paclitaxel combination, was based on the observation that reparixin treatment contained the formation of metastases in several experimental models. However, specific data on the formation of breast cancer brain metastases, which carry remarkable morbidity and mortality to a substantial proportion of advanced breast cancer patients, have not been generated. The obtained data indicate a beneficial use of the drug combination reparixin and paclitaxel to counteract brain tumour metastasis due to CSC, probably due to the combined effects of the two drugs, the pro-apoptotic action of paclitaxel and the cytostatic and anti-migratory effects of reparixin.

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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. *

Using an approach to analyze the θ dependence of systems with a θ-term we recently proposed , the critical behavior of CP 1 at θ = π is studied. We find a region outside the strong coupling regime where Haldane's conjecture is verified. The critical line however does not belong to the universality class of the Wess-Zumino-Novikov-Witten model at topological coupling k = 1 since it shows continuously varying critical exponents.