We investigate the topological properties of N f = 2 + 1 QCD with physical quark masses, both at zero and finite temperature. We adopt stout improved staggered fermions and explore a range of lattice spacings a ∼ 0.05− 0.12 fm. At zero temperature we estimate both finite size and finite cut-off effects, comparing our continuum extrapolated results for the topological susceptibility χ with predictions from chiral perturbation theory. At finite temperature, we explore a region going from T c up to around 4 T c , where we provide continuum extrapolated results for the topological susceptibility and for the fourth moment of the topological charge distribution. While the latter converges to the dilute instanton gas prediction the former differs strongly both in the size and in the temperature dependence. This results in a shift of the axion dark matter window of almost one order of magnitude with respect to the instanton computation.

We investigate the static Q¯Q potential for Nf=2+1 QCD at the physical point in the presence of a constant and uniform external magnetic field. The potential is found to be anisotropic and steeper in the directions transverse to the magnetic field than in the longitudinal one. In particular, when compared to the standard case with zero background field, the string tension increases (decreases) in the transverse (longitudinal) direction, while the absolute value of the Coulomb coupling and the Sommer parameter show an opposite behavior

We perform lattice studies of meson mass spectra and decay constants of the Sp(4) gauge theory in the quenched approximation. We consider two species of (Dirac) fermions as matter field content, transforming in the 2-index antisymmetric and the fundamental representation of the gauge group, respectively. All matter fields are formulated as Wilson fermions. We extrapolate to the continuum and massless limits, and compare to each other the results obtained for the two species of mesons. In the case of two fundamental and three antisymmetric fermions, the long-distance dynamics is relevant for composite Higgs models. This is the first lattice study of this class of theories. The global SU (4) × SU (6) symmetry is broken to the Sp(4) × SO(6) subgroup, and the condensates align with the explicit mass terms present in the lattice formulation of the theory.The main results of our quenched calculations are that, with fermions in the 2-index antisymmetric representation of the group, the masses squared and decay constant squared of all the mesons we considered are larger than the corresponding quantities for the fundamental representation, by factors that vary between ∼ 1.2 and ∼ 2.7. We also present technical results that will be useful for future lattice investigations of dynamical simulations, of composite chimera baryons, and of the approach to large-N in the Sp(2N ) theories considered. We briefly discuss their high-temperature behaviour, where symmetry restoration and enhancement are expected. We acknowledge useful discussions withWe summarise in this Appendix our conventions in the treatment of spinors, which are useful, for example, in switching between the 2-component and the 4-component notation (see also Ref. [50]). The former is best suited to highlight the symmetries of the system, while the latter is the formalism adopted as a starting point for the lattice numerical