RENORMALIZATION-GROUP FLOW AND FIXED-POINT OF THE LATTICE TOPOLOGICALCHARGE IN THE 2D O(3) SIGMA-MODEL

We study the renormalization group evolution up to the fixed point of the lattice topological susceptibility in the 2D O(3) nonlinear a mode l. We start with a discretization of the continuum topological charge by a local charge density polynomial in the lattice fields. Among the different choices we propose also a Symanzik-improved lattice topologi cal charge. We check step by step in the renormalization group iterati on the progressive dumping of quantum fluctuations, which are responsi ble for the additive and multiplicative renormalizations of the lattic e topological susceptibility with respect to the continuum definition. We find that already after three iterations these renormalizations ar e negligible and an excellent approximation of the fixed point is achi eved. We also check by an explicit calculation that the assumption of slowly varying fields in iterating the renormalization group does not lead to a good approximation of the fixed point charge operator.