Dyson-Schwinger Equations in Minimal Subtraction. arXiv:2109.13684
Preprint, arXiv:2109.13684 [hep-th] (2021).
Summary: We compare the solutions of one-scale Dyson-Schwinger equations in the Minimal subtraction (MS) scheme to the solutions in kinematic (MOM) renormalization schemes. We establish that the MS-solution can be interpreted as a MOM-solution, but with a shifted renormalization point, where the shift itself is a function of the coupling. We derive relations between this shift and various renormalization group functions and counter terms in perturbation theory. As concrete examples, we examine three different one-scale Dyson-Schwinger equations, one based on the D=4 multiedge graph, one for the D=6 multiedge graph and one mathematical toy model. For each of the integral kernels, we examine both the linear and nine different non-linear Dyson-Schwinger equations. For the linear cases, we empirically find exact functional forms of the shift between MOM and MS renormalization points. For the non-linear DSEs, the results for the shift suggest a factorially divergent power series. We determine the leading asymptotic growth parameters and find them in agreement with the ones of the anomalous dimension. Finally, we present a tentative exact non-perturbative solution to one of the non-linear DSEs of the toy model.
MSC:
81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
45M05 | Asymptotics of solutions to integral equations |
81T17 | Renormalization group methods applied to problems in quantum field theory |
40G10 | Abel, Borel and power series methods |
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