1991/09/24 by Andrea Cappelli, José Ignacio Latorre, J. I. Latorre +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1016/0550-3213(92)90119-v
published as Nucl.Phys. B376 (1992) 510-538 · 33 pages
arxiv created 1991/09/24 · openalex publication_date 1992/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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≤ d≤ 4 and large N.