Renormalization of the theta angle, the quantum Hall effect, and the strong CP problem

We discuss the need for and consequences of non-perturbative renormalizations of couplings including the vacuum theta angle. An explicit example of these effects is found in the recently proposed scaling theory of the integral quantum Hall effect. In that theory the theta angle has a precise parallel in the value of the Hall conductivity sigmasub(xy) which flows from its CPA (short distance) value to quantization at macroscopic distances. We further comment that such theta scaling phenomena provide a mechanism for strong CP conservation. (orig.)