Strong CP problem, electric dipole moment, and fate of the axion

Three hard problems! In this talk I investigate the long-distance properties of quantum chromodynamics in the presence of a topological theta term. This is done on the lattice, using the gradient flow to isolate the long-distance modes in the functional integral measure and tracing it over successive length scales. It turns out that the color fields produced by quarks and gluons are screened, and confinement is lost, for vacuum angles theta > 0, thus providing a natural solution of the strong CP problem. This solution is compatible with recent lattice calculations of the electric dipole moment of the neutron, while it excludes the axion extension of the Standard Model.