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arXiv · hep-th/9109041

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

Andrea Cappelli·José Ignacio Latorre·Xavier Vilasis-Cardona
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Abstract

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 $2<d<4$. We also discuss the non-perturbative flows in the yet unsettled case of the $O(N)$ sigma-model for $2\leq d\leq 4$ and large $N$.

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Andrea Cappelli, José Ignacio Latorre, Xavier Vilasis-Cardona. 1991-09-24. Renormalization Group Patterns and C-Theorem in More Than Two Dimensions. https://doi.org/10.1016/0550-3213(92)90119-v

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