C-theorem

C-theorem

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.

ee also

*Conformal field theory

References

*A.B Zamolodchikov, ``Irreversibility' Of The Flux Of The Renormalization Group In A 2-D Field Theory, JETP Lett.43:730-732,1986.

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