Dimensional Renormalization in phi^3 theory: ladders and rainbows

Details Dimensional Renormalization in phi^3 theory: ladders and rainbows Dimensional Renormalization in phi^3 theory: ladders and rainbows

1996-11-20

arxiv.org/abs/hep-th/9611150v1

Phys.Rev.D55:5230-5233,1997

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX, no figures

Scientific paper

10.1103/PhysRevD.55.5230

The sum of all ladder and rainbow diagrams in $\phi^3$ theory near 6 dimensions leads to self-consistent higher order differential equations in coordinate space which are not particularly simple for arbitrary dimension D. We have now succeeded in solving these equations, expressing the results in terms of generalized hypergeometric functions; the expansion and representation of these functions can then be used to prove the absence of renormalization factors which are transcendental for this theory and this topology to all orders in perturbation theory. The correct anomalous scaling dimensions of the Green functions are also obtained in the six-dimensional limit.

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