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The vacuum of quantum chromodynamics has an incredibly rich structure at thenonperturbative level, which is intimately connected with the topology of gaugefields, and put to a test by the strong CP problem. We investigate thelong-distance properties of the theory in the presence of the topological$\theta$ term. This is done on the lattice, using the gradient flow to isolatethe long-distance modes in the functional integral measure and tracing it oversuccessive length scales. The key point is that the vacuum splits intodisconnected topological sectors with markedly different physicalcharacteristics, which gives rise to a nontrivial behavior depending on$\theta$. We find that the color fields produced by quarks and gluons arescreened, and confinement is lost, for bare vacuum angles $|\theta| > 0$, thusproviding a natural solution of the strong CP problem. The renormalized vacuumangle $\theta$ is found to flow to zero in the infrared limit, leading to aself-consistent solution within QCD.

The strong CP problem solved by itself due to long-distance vacuum effects