Reduction of the N-component scalar model at the two-loop level

Dimensional reduction of high temperature field theories improves IR features of their perturbative treatment. A crucial question is the following: What three-dimensional theory is representing the full system the most faithful way? A careful investigation of the induced three-dimensional counterterm structure of the finite temperature 4D O(N) symmetric scalar theory at the two-loop level leads to proposing the presence of nonlocal operators in the effective theory. A three-dimensional matching process is applied for the construction of the optimal local, superrenormalizable approximation.