increases as the scale increases. The renormalized coupling constant, which changes with the energy scale, is also called the running coupling constant. The coupling constant in quantum chromodynamics, a non-Abelian gauge theory based on the symmetry group , has the following β function: where is the number of quark flavours. In the case where (the Standard Model has ), the coupling constant decreases as the energy scale increases. Hence, while the strong interaction is strong at low energies, it becomes very weak in high-energy interactions, a phenomenon known as asymptotic freedom. Conformal field theories (CFTs) are special QFTs that admit conformal symmetry. They are insensitive to changes in the scale, as all their coupling constants have vanishing β function. (The converse is not true, however — the vanishing of all β functions does not imply conformal symmetry of the theory.) Examples include string theory and supersymmetric Yang–Mills theory. According to Wilson's picture, every QFT is fundamentally accompanied by its energy cut-off , i.e. that the theory is no longer valid at energies higher than , and all degrees of freedom above the scale are to be omitted. For example, the cut-off could be the inverse of the atomic spacing in a condensed matter system, and in elementary particle physics it could be associated with the fundamental "graininess" of spacetime caused by quantum fluctuations in gravity. The cut-off scale of theories of particle interactions lies far beyond current experiments. Even if the theory were very complicated at that scale, as long as its couplings are sufficiently weak, it must be described at low energies by a renormalizable effective field theory. The difference between renormalizable and non-renormalizable theories is that the former are insensitive to details at high energies, whereas the latter do depend on them. According to this view, non-renormalizable theories are to be seen as low-energy effective theories of a more fundamental theory. The failure to remove the cut-off from calculations in such a theory merely indicates that new physical phenomena appear at scales above , where a new theory is necessary. Other theories The quantization and renormalization procedures outlined in the preceding sections are performed for the free theory and theory of the real scalar field. A similar process can be done for other types of fields, including the complex scalar field, the vector field, and the Dirac field, as well as other types of interaction terms, including the