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 $C{P}^3$. 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.

Targeting CXCR1 on breast cancer stem cells: signaling pathways and clinical application modelling

In this article we elaborate on a recently proposed interpretation of deformed special relativity (DSR) as an effective measurement theory in the presence of non-negligible (albeit small) quantum gravitational fluctuations. We provide several heuristic arguments to explain how such a new theory can emerge and discuss the possible observational consequences of this framework. Given that our discussion considers leading order corrections to the standard dispersion relations, our results apply to a very wide class of possible modifications of special relativity.

We show that an essential assumption in the Vafa-Witten theorem on $P$ and $\mathrm{CT}$ realization in vectorlike 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.