Unrenormalizable Theories Can Be Predictive

Details Unrenormalizable Theories Can Be Predictive Unrenormalizable Theories Can Be Predictive

2001-12-05

arxiv.org/abs/hep-th/0112032v2

Eur.Phys.J. C26 (2003) 461-472

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, TeX, 14 figures

Scientific paper

10.1140/epjc/s2002-01022-5

Unrenormalizable theories contain infinitely many free parameters. Considering these theories in terms of the Wilsonian renormalization group (RG), we suggest a method for removing this large ambiguity. Our basic assumption is the existence of the maximal ultraviolet cutoff in a cutoff theory, and we require that the theory be so fine-tuned as to reach the maximal cutoff. The theory so obtained behaves as a local continuum theory to the shortest distance. In concrete examples of the scalar theory we find that at least in a certain approximation to the Wilsonian RG, this requirement enable us to make unique predictions in the infrared regime in terms of a finite number of independent parameters. Therefore, the method might provide a way for calculating quantum corrections in a low-energy effective theory of quantum gravity.

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