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Renormalization is an essential feature of both effective field theory (EFT) and conformal field theory (CFT). In EFT, the anomalous dimensions determine the parameters’ dependence on the energy scale of the process. At the conformal fixed point, the same quantities become directly observable as they determine the spectrum of the theory. I will present the perturbative renormalization of general scalar theories in 4-ε spacetime dimensions. Our results are of direct relevance for real-world critical phenomena in three dimensions (ε=1), when applied to specific theories such as the Ising model and the O(n) CFT. Moreover, our insight on the spectrum of more complicated theories paves the way for future non-perturbative studies.
