Infrared behavior of the running coupling in scalar field theory

Details Infrared behavior of the running coupling in scalar field theory Infrared behavior of the running coupling in scalar field theory

2008-02-08

arxiv.org/abs/0802.1183v4

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, 2 figures. Completely revised version introducing for the first time a covariant version of our strong coupling expa

Scientific paper

We compute the Green function of the massless scalar field theory in the infrared till the next-to-leading order, providing a fully covariant strong coupling expansion. Applying Callan-Symanzik equation we obtain the exact running coupling for this case by computing the beta function. This result is applied using a recently proved mapping theorem between a massless scalar field theory and Yang-Mills theory. This beta function gives a running coupling going to zero as $p^4$ in agreement with lattice results presented in Boucaud et al. [JHEP 0304 (2003) 005] and showing that the right definition of the running coupling for a Yang-Mills theory in the infrared is given in a MOM scheme. The emerging scenario is supporting a quantum field theory based on instantons.

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