Approaches to Quantum Gravity

230 Questions and answers3. You state that the AdS/CFT correspondence provides a background independentformulation of Quantum Gravity in terms of the dual gauge theory, forgiven boundary. Let me understand better the statement, given that backgroundindependence is such a crucial notion in all Quantum Gravity approaches,including of course string theory. If I was to re-phrase the quantum dynamicsof the gravitational degrees of freedom as encoded in the AdS/CFT, i.e. asdescribed by the dual gauge theory, in the form of a path integral for QuantumGravity, should I think of it as given by a sum over all possible geometries, atfixed topology, for given boundary conditions (the flat 4d Minkowski geometry),or rather by a sum over all possible geometries, at fixed topology, for givenboundary conditions ∗ and ∗ given asymptotic behaviour of the geometries? In thefirst case, indeed, one would have a full definition of the gravitational path integral,for given boundary, while the second would incorporate also a (admittedlymild) restriction on the configurations summed over.– A-G.HorowitzandJ.Polchinski:1. We disagree that your options are mutually exclusive. Certainly the thirdoption is true: AdS/CFT and other dualities are statements about mathematicalphysics, which can be used to derive relations between the spectrum,amplitudes, and other physical properties of the two sides of the duality. However,we disagree with the premise that only one side of a duality can be“real”. In electric–magnetic duality in quantum field theory, both the electricalcharges and the magnetic charges are “real”. There is simply one classicallimit described in terms of electrically charged fields, and the quantum theoryconstructed as a path integral over such fields, and another classical limitdescribed in terms of magnetically charged fields, and the quantum theoryconstructed as a path integral over these fields. One is just making a changeof variables, neither description is more “real”. In the AdS/CFT case, the situationmay not be so symmetric, in that for now the gauge side has an exactdescription and the string/gravity side only an approximate one: we mighttake the point of view that strings and spacetime are “emergent” and that theultimate precise description of the theory will be in variables closer to the CFTform. “Emergent”, however, is not the opposite of “real”: most phenomena innature are emergent, but nevertheless real. In particular, since we experiencegravity, it would be this emergent description that is real to us.2. At the moment, AdS/CFT does not shed any light on the cosmologicalconstant. The best explanation that string theory can provide at the momentcomes from the large number of classical vacua (the “landscape”).3. Neither of your descriptions is correct since the path integral in the bulkincludes a sum over topologies as well as metrics. In terms of the boundary