Renormalization Group Patterns and C-Theorem in More Than Two Dimensions

Details Renormalization Group Patterns and C-Theorem in More Than Two Dimensions Renormalization Group Patterns and C-Theorem in More Than Two Dimensions

1991-09-24

arxiv.org/abs/hep-th/9109041v1

Nucl.Phys. B376 (1992) 510-538

Physics

High Energy Physics

High Energy Physics - Theory

33 pages

Scientific paper

10.1016/0550-3213(92)90119-V

We elaborate on a previous attempt to prove the irreversibility of the renormalization group flow above two dimensions. This involves the construction of a monotonically decreasing $c$-function using a spectral representation. The missing step of the proof is a good definition of this function at the fixed points. We argue that for all kinds of perturbative flows the $c$-function is well-defined and the $c$-theorem holds in any dimension. We provide examples in multicritical and multicomponent scalar theories for dimension $2

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