Approaches to Quantum Gravity

190 T. BanksThis lightning review of results from string theory 3 was supposed to make thereader realize that existing forms of string theory are disconnected from each other,and that the unique features of each example depend on the asymptotic geometryof space-time. We should expect the same to be true in more complicated situations,and should be particularly wary of cases, like Big Bangs and Crunches, andde Sitter space, where the boundaries are not all under control. It is my opinion thatthe study of cosmology and/or de Sitter space, requires us to go beyond conventionalstring theory. Unless one believes in Big Bounce scenarios, in which thereis an asymptotically infinite past, then cosmology cannot be described by a real S-matrix. There is an initial space-like hypersurface, a finite proper time in the past ofall observers. The initial state describing this configuration may be uniquely determined,from first principles (I call this an S-vector scenario), or must be chosen atrandom subject to some constraints. In neither case does conventional string theoryhave to be a valid description near the Big Bang. Attempts to apply conventionalstring theory techniques to model cosmologies have not met with success.Similarly, if the final state of the universe is a stable, asymptotically de Sitterspace, then the scattering boundary conditions of string theory are not applicableeither (though something approximating them for small might be appropriate). 4I believe that, in order to formulate a more general theory of Quantum Gravity,which will enable us to cope with cosmological situations, we must find a descriptionanalogous to the local field theory description of classical gravitation. Thisformalism works with non-gauge invariant quantities because there are no gaugeinvariant local observables in diffeomorphism invariant theories. The quantum formalismI propose will be similar, and will be tied to a fixed physical gauge, whichin the semi-classical limit should be thought of as the coordinate system of a giventime-like observer. I will use the word observer to denote a large quantum systemwith a wealth of observables whose quantum fluctuations are exponentially smallas a function of a macroscopic volume parameter. Systems well described by (perhapscut-off) quantum field theory provide us with many examples of observers inthis sense. Note that an observer need have neither gender nor consciousness.Local physics in generally covariant theories is either gauge variant or definedby a given classical background. There can be no gauge invariant quantum notionof locality in the quantum theory of gravity. But there is no reason why we cannotintroduce local or quasi-local concepts which are tied to a particular referenceframe/gauge choice. Indeed, all local physics in the real world is based on the existenceof a regime where we can have large classical objects, which do not collapse3 A more extensive discussion of string dualities and AdS/CFT can be found in the chapter by Horowitz andPolchinski and in the references cited there.4 I am giving short shrift here to the idea of dS/CFT [9; 10; 11]. I do not believe this formalism actually makessense, but it deserves more of a discussion than I have space for here.