Approaches to Quantum Gravity

Questions and answers 161the action for is just a mass term, implying that vanishes on shell. Inthis case one expects the flow to be essentially equivalent to that obtainedin the Einstein–Hilbert truncation plus some matter fields, although thishas not been explicitly checked yet. The presence of a mass for of theorder of the Planck mass suggests that a decoupling theorem is at work andthat (or equivalently the connection) will become propagating degreesof freedom at the Planck scale. This is indeed the case when the actioninvolves terms quadratic in curvature (which can be neglected at low energies).Then the field propagates, and has quartic self-interactions. Therewill be new couplings, that may influence the running of Newton’s constant,for example. But again, this should be equivalent to fourth-order gravity plusmatter.3. I do in fact expect that an independent connection will manifest itself at thePlanck scale, as I have indicated in my answer to another question, though Idon’t think that this will be forced upon us by the ERG.The scale-dependence of the metric could manifest itself as violations of theequivalence principle, or perhaps as Lorentz-invariance violations or deformationsof the Lorentz group. There is much work to be done to understandthis type of phenomenology. Even more radically, it is possible that gravityis just the “low energy” manifestation of some completely different physics,as suggested in the article by Dreyer. This would probably imply a failure ofthe asymptotic safety programme, for example a failure to find a fixed pointwhen certain couplings are considered.4. So far the ERG has been applied to gravity in conjunction with thebackground field method. Calculations are often performed in a convenientbackground, such as (Euclidean) de Sitter space, but the beta functionsobtained in this way are then completely general and independent of the backgroundmetric and spacetime topology. The choice of a background is merelya calculational trick. It is assumed that the beta functions are also independentof the signature of the background metric, although this point may require furtherjustification. One should also stress in this connection that the use of thebackground field method and of the background field gauge does not makethis a “background-dependent” approach. On the contrary, when properlyimplemented it guarantees that the results are background-independent.• Q - F. Girelli - to R. Percacci:Could an asymptotically safe theory be regarded as an approximation toanother more fundamental theory, or does it have to be regarded as a selfcontainedfundamental theory?