Approaches to Quantum Gravity

String theory, holography and Quantum Gravity 205Each integer from 1 to M denotes states in one of M horizon volumes. The statesin a given block correspond to “single particle states”, and the multiple blockswith the same label are multiple particles in a single horizon volume, much as inMatrix Theory [28]. Work in progress [29] will show that the single particle statesin this description indeed correspond to states of a massless N = 1 supermultipletdescribed at null infinity. The sphere at null infinity is fuzzy [30] for finite R,corresponding to the cut off on particle momenta in the field theory discussion.As in Matrix Theory, the size of the block representing a single particle measuresits longitudinal momentum along a particular null direction, while the state of thefermionic variables corresponding to the block determines the spin and angularwave functions of the particle on the sphere at null infinity. The Matrix Theory formalismwas contructed on a light front, and all longitudinal momenta were alignedin the same direction. Here, each particle carries its own longitudinal direction,which identifies the pixel via which it enters or exits the holographic screen.This formalism is more flexible than cut-off field theory. It can describe particlesof large momentum in a given horizon volume by making one of the blocks ina given horizon much larger than M. The price for this is paid by having fewerparticles, or by forcing the other particles to have low momentum.One of the intriguing features of this conjecture about the way in whichsuper-Poincaré invariant particle physics will emerge from the formulation of thequantum theory of dS space in terms of fermionic pixels, is the natural appearanceof the variable M = √ N. This is the variable which controls the fuzziness of thegeometry of the momentum space spheres of individual particles. We hope to show[29] that the theory becomes super-Poincaré invariant in the limit M →∞, withcorrections of order 1 . In particular, this would imply thatM[P 0 , Q α ]∼o( 1 M ).In spontaneously broken low energy SUGRA, the superpartner of a given particle isa two particle state with an extra zero-momentum gravitino. The splitting betweenthese states is just the gravitino mass. Thus, taken at face value, the above equationsays that the gravitino mass scales like 1 M∼ 1/4 . This is the scaling relation Ipostulated under the name Cosmological SUSY Breaking [17]. It predicts superpartnermasses in the TeV energy range and has numerous implications for lowenergy physics and dark matter.11.4 SummaryString theory has provided us with extensive evidence for the existence of modelsof Quantum Gravity in asymptotically flat and AdS space-times. In the AdS case