REDUCTION OF THE N-COMPONENT SCALAR MODEL AT TWO LOOP LEVEL

Dimensional reduction of high temperature field theories improves IR features of their perturbative treatment. A crucial question is, what three-dimensional theory is representing the full system the most faithful way. Careful investigation of the induced 3-dimensional counterterm structure of the finite temperature 4D O(N) symmetric scalar theory at 2-loop level leads to proposing the presence of non-local operators in the effective theory. On scales beyond $\mathcal{O}(T^{-1})$, the scaling behavior of the couplings, consequently, deviates from the usual three-dimensional scaling characteristic for superrenormalizable theories.