Investigating the Ultraviolet Properties of Gravity with a W(3)

We review and extend in several directions recent results on the asymptotic safety approach to quantum gravity. The central issue in this approach is the search of a Fixed Point having suitable properties, and the tool that is used is a type of Wilsonian r

I.INTRODUCTIONItiswellknownthatgeneralrelativitycanbetreatedasane ectivequantum eldtheory

[1,2,4].Thismeansthatitispossibletocomputequantume ectsduetogravitonloops,aslongasthemomentumoftheparticlesintheloopsiscuto atsomescale.Forexample,inthiswayithasbeenpossibletounambiguouslycomputequantumcorrectionstotheNewtonianpotential[2].Theresultsareindependentofthestructureofany“ultravioletcompletion”,andthereforeconstitutegenuinelowenergypredictionsofanyquantumtheoryofgravity.Whenonetriestopushthise ective eldtheorytoenergyscalescomparabletothePlanckscale,orbeyond,well-knowndi cultiesappear.Itisconvenienttodistinguishtwoordersofproblems.The rstisthatthestrengthofthegravitationalcouplinggrowswithoutbound.Foraparticlewithenergypthee ectivestrengthofthegravitational couplingismeasuredbythedimensionlessnumber

1Strictlyspeakingonlytheessentialcouplings,i.e.thosethatcannotbeeliminatedby eldrede nitions,needtoreachaFP.See[3]forarelateddiscussioninagravitationalcontext.