We present an ab initio study of inclusive semileptonic decays of heavy mesons from lattice QCD. Our approach is based on a recently proposed method, that allows one to address the study of these decays from the analysis of smeared spectral functions extracted from four-point correlators on the lattice, where the smearing is defined in terms of the phase-space integration relevant to the inclusive decays. We present results obtained from gauge-field ensembles from the JLQCD and ETM collaborations, and discuss their relation with theoretical predictions from the operator-product expansion.

We present a high-precision Monte Carlo study of the classical Heisenberg model in four dimensions. We investigate the properties of monopole-like topological excitations that are enforced in the broken-symmetry phase by imposing suitable boundary conditions. We show that the corresponding magnetization and energy-density profiles are accurately predicted by previous analytical calculations derived in quantum field theory, while the scaling of the low-energy parameters of this description questions an interpretation in terms of particle excitations. We discuss the relevance of these findings and their possible experimental applications in condensed-matter physics.

We present a study of the effective string that describes the infrared dynamics of SU(2) Yang-Mills theory in three dimensions. By combining high-precision lattice simulation results for Polyakov-loop correlators at finite temperatures close to (and less than) the deconfinement one with the analytical constraints from renormalization-group arguments, from the exact integrability of the two-dimensional Ising model that describes the universality class of the critical point of the theory, from conformal perturbation theory, and from Lorentz invariance, we derive tight quantitative bounds on the corrections to the effective string action beyond the Nambu-Gotō approximation. We show that these corrections are compatible with the predictions derived from a bootstrap analysis of the effective string theory, and have a value which does not allow to prove the Axionic String Ansatz for this model.

We present the lattice QCD calculation of inclusive semileptonic B s -meson decays. We follow a recently proposed method, which is based on the extraction of smeared spectral densities from Euclidean correlation functions and on the numerical reconstruction of the integration kernel relevant for the inclusive decay rate calculation. We compute four-point Euclidean correlation functions using JLQCD and ETM gauge ensembles with unphysically light b-quark masses, and apply two different methods for the integration kernel reconstruction. Finally, we show that the lattice results obtained in this work are in good agreement with the analytic predictions of the operator-product-expansion. This opens the path for a future full lattice QCD calculation to be used as theoretical input for the determination of the magnitude of the CKM element V cb .

We present a high-precision Monte Carlo study of the O(3) spin theory on the lattice in D = 4 dimensions. This model exhibits interesting dynamical features, in particular in the brokensymmetry phase, where suitable boundary conditions can be used to enforce monopole-like topological excitations. We investigate the Euclidean time propagation and the features of these excitations close to the critical point, where our numerical results show an excellent quantitative agreement with analytic predictions derived from purely quantum-field-theoretical tools by G. Delfino. We conclude by commenting on the implications of our findings for a conjectured violation of Derrick's theorem at the quantum level and on the consequences in various areas of physics, ranging from condensed matter to astro-particle physics.