Approaches to Quantum Gravity

184 G. Horowitz and J. Polchinskican be understood as a conflict between quantum mechanics and locality. In thecontext of emergent spacetime it is not surprising that it is locality that yields, butwe would like to understand the precise manner in which it does so.A big open question is how to extend all this from AdS boundary conditions tospacetimes that are more relevant to nature; we did find some generalizations, butthey all have a causal structure similar to that of AdS. Again, the goal is a preciselydefined nonperturbative construction of the theory, presumably with the same featuresof emergence that we have found in the AdS/CFT case. A natural next stepmight seem to be de Sitter space. There were some attempts along these lines, forexample [37; 44], but there are also general arguments that this idea is problematic[39]. In fact, this may be the wrong question, as constructions of de Sittervacua in string theory (beginning with [36; 23]) always seem to produce statesthat are only metastable (see [14], for further discussion, and [3], for an alternateview). As a result, cosmology will produce a chaotic state with bubbles of all possiblemetastable vacua [8]. The question is then the nonperturbative construction ofstates of this kind. The only obvious spacetime boundaries are in the infinite future,in eternal bubbles of zero cosmological constant (and possibly similar boundariesin the infinite past). By analogy these would be the location of the holographic dualvariables [39].In conclusion, the embedding of Quantum Gravity in ordinary gauge theory isa remarkable and unexpected property of the mathematical structures underlyingtheoretical physics. We find it difficult to believe that nature does not make use ofit, but the precise way in which it does so remains to be discovered.AcknowledgmentsThis work was supported in part by NSF grants PHY99-07949, PHY02-44764, andPHY04-56556.References[1] O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri & Y. Oz, Large N fieldtheories, string theory and gravity. Phys. Rept. 323 (2000) 183[arXiv:hep-th/9905111].[2] F. Antonuccio, A. Hashimoto, O. Lunin & S. Pinsky, Can DLCQ test the Maldacenaconjecture? JHEP 9907 (1999) 029 [arXiv:hep-th/9906087].[3] T. Banks, More thoughts on the quantum theory of stable de Sitter space (2005)arXiv:hep-th/0503066.[4] G. Baskaran & P. W. Anderson, Gauge theory of high temperature superconductorsand strongly correlated Fermi systems. Phys. Rev. B 37 (1988) 580.[5] D. Berenstein, J. M. Maldacena & H. Nastase, Strings in flat space and pp wavesfrom N = 4 super Yang Mills. JHEP 0204 (2002) 013 [arXiv:hep-th/0202021].