Effective field theory of gravity, reduction of couplings, and the renormalization group

Abstract

The structure of the renormalization group equations for the low-energy effective theory of gravity coupled to a scalar field is presented. An approximate solution to these equations with a finite number of independent renormalized parameters can be found when the mass scale characteristic of the fluctuations in the geometry is much smaller than the Planck mass. The cosmological constant problem is reformulated in this context and some conditions on the matter field content and interactions required in order to have a sufficiently small cosmological constant are identified. ͓S0556-2821͑96͒06320-5͔

The asymptotic safety scenario in quantum gravity: an introduction

“…A number of authors have argued in the effective field theory framework that even theories with an infinite number of relevant parameters can be predictive [92,13,27]. This applies all the more if the theory under consideration is based on a fixed point, and thus not merely effective.…”

“…One reason lies in the fact the number of independent relevant directions connected to the fixed point might not be known. Hidden dependencies would then allow for a (genuine or effective) reduction of couplings [159,113,123,9,13]. For quantum gravity the situation is further complicated by the fact that generic physical quantities are likely to be related only nonlocally and nonlinearly to the metric.…”

“…All choices lead to flow equation of the form 13) but the coefficient γ depends on the choice of the reference operator [85]. For all γ > 0 there is a nontrivial fixed point g * N = ǫ/γ > 0 with a one-dimensional unstable manifold.…”

Effective scalar field theory and reduction of couplings

“…In previous works [12,13] the authors considered the possibility to apply the method of reduction of couplings to the effective field theoretic formulation of quantum gravity. The nonrenormalizability of the theory is not an obstacle to identifying a theory with a finite number of independent parameters.…”

Unrenormalizable theories can be predictive

“…Indeed, except for (3.32) and (3.34), which now become 13 Application of reduction of coupling constants to quantum gravity has been considered in Ref. [26]. See also [27].…”