Beta function and flowing couplings in the exact Wilson renormalization group in Yang-Mills theory

DOI10.1016/S0550-3213(96)00571-8zbMATH Open0925.81111arXivhep-th/9604114OpenAlexW2950656862MaRDI QIDQ1816807

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Publication date: 28 November 1996

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Abstract: We discuss the relation between the Gell-Mann-Low beta function and the ``flowing couplings of the Wilsonian action $S_{L} [p h i]$ of the exact renormalization group (RG) at the scale $L$ . This relation involves the ultraviolet region of $L$ so that the condition of renormalizability is equivalent to the Callan-Symanzik equation. As an illustration, by using the exact RG formulation, we compute the beta function in Yang-Mills theory to one loop (and to two loops for the scalar case). We also study the infrared (IR) renormalons. This formulation is particularly suited for this study since: $i$ ) $L$ plays the r^ole of a IR cutoff in Feynman diagrams and non-perturbative effects could be generated as soon as $L$ becomes small; $i i$ ) by a systematical resummation of higher order corrections the Wilsonian flowing couplings enter directly into the Feynman diagrams with a scale given by the internal loop momenta; $i i i$ ) these couplings tend to the running coupling at high frequency, they differ at low frequency and remain finite all the way down to zero frequency.

Full work available at URL: https://arxiv.org/abs/hep-th/9604114

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