C-theorem

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In theoretical physics, specifically quantum field theory, a C-theorem states that there exists a function, $C(g^{}_i,\mu)$ , depending on the coupling constants of the quantum field theory, $g^{}_i$ , and on the energy scale, $\mu^{}_{}$ , which has the following properties:

$C(g^{}_i,\mu)$ decreases monotonically under renormalization group (RG) flow.

At fixed points of the RG flow, which are specified by a set of fixed-point couplings $g^*_i$ , the function $C(g^*_i,\mu)=C_*$ is a constant, independent of energy scale.

If such a so-called C-function exists for a given quantum field theory, it tells us that the RG flow of the theory is irreversible.

Zamolodchikov proved that two-dimensional quantum field theory always has a C-function. Moreover, at fixed points, Zamolodchikov's C-function is equal to the central charge of the corresponding conformal field theory.

It has not yet been possible to prove a C-theorem in higher-dimensional quantum field theory.