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Toy Models of Non-perturbative Asymptotic Freedom in $ϕ^3_6$

John M. Cornwall·Duncan A. Morris
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Abstract

We study idealizations of the full nonlinear Schwinger-Dyson equations for the asymptotically free theory of $ϕ^3$ in six dimensions in its meta-stable vacuum. We begin with the cubic nonlinearity and go on to all-order nonlinearities which contain instanton effects. We show how our toy models of the cubic Schwinger-Dyson equations contain the usual diseases of perturbation theory in the massless limit (e.g., factorially divergent $β-$functions, singular Borel-transform kernels associated with infrared renormalons) and show how these models yield specific mechanisms for removing such singularities when there is a mass gap. In the all-order nonlinear equation we show how to recover the usual renormalization-group-improved instanton effects and associated factorial divergences.

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John M. Cornwall, Duncan A. Morris. 1995-06-11. Toy Models of Non-perturbative Asymptotic Freedom in $ϕ^3_6$. https://doi.org/10.1103/physrevd.52.6074

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