Approaches to Quantum Gravity

11String theory, holography and Quantum GravityT. BANKS11.1 IntroductionIt is the opinion of this author that many theories of Quantum Gravity have alreadybeen discovered, but that the one which applies to the real world still remains amystery. The theories I am referring to all go under the rubric of M/string-theory,and most practitioners of this discipline would claim that they are all “vacuumstates of a single theory". The model for such a claim is a quantum field theorywhose effective potential has many degenerate minima, but I believe this analogyis profoundly misleading.Among these theories are some which live in asymptotically flat space-times ofdimensions between 11 and 4. The gauge invariant observables of these theoriesare encoded in a scattering matrix. 1 All of these theories are exactly supersymmetric,a fact that I consider to be an important clue to the physics of the real world.In addition, they all have continuous families of deformations. These families arevery close to being analogs of the moduli spaces of vacuum states of supersymmetricquantum field theory. They all have the same high energy behavior, and one cancreate excitations at one value of the moduli which imitate the physics at anothervalue, over an arbitrarily large region of space. Except for the maximally supersymmetriccase, there is no argument that all of these models are connected by varyingmoduli in this way. One other feature of these models is noteworthy. Some of themare related to others by compactification, e.g. the same low energy Lagrangianappears on R 1,10−D ×T D , for various values of D. It is always the case that the modelswith more compact dimensions have more fundamental degrees of freedom.1 In four dimensions, the gravitational scattering matrix has familiar infrared divergences. It is believed by manythat this is a technical problem, which is more or less understood. There can also be problems with confininggauge theories, whose resolution in a purely S-matrix context is somewhat obscure. String perturbation theoryfor four dimensional compactifications instructs us to compute gauge boson scattering amplitudes, whichprobably do not exist.Approaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter, ed. Daniele Oriti.Published by Cambridge University Press. c○ Cambridge University Press 2009.