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Renormalization group patterns and c-theorem in more than two dimensions

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 th...

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Detalles Bibliográficos
Autores principales: Cappelli, Andrea, Latorre, Jose Ignacio, Vilasis-Cardona, Xavier
Lenguaje:eng
Publicado: 1992
Materias:
Acceso en línea:https://dx.doi.org/10.1016/0550-3213(92)90119-V
http://cds.cern.ch/record/225418
Descripción
Sumario: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 $N$.