100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

332 T. Banksthat there is a positive c.c., it is certainly the simplest explanation of whatis seen. Positive c.c. is a theoretical conundrum for the present form ofstring theory. Asymptotic dS spaces do not admit the kinds of boundaryobservables that string theory can calculate.There have been two kinds of reaction to this in the string theory community.The first was to try to create a generalization of string theory tocope with dS space 37 . I still believe that is the correct path, although somepessimistic conclusions have appeared in the literature 38 , and I will returnto this below. The second was driven by the discovery of an apparent solutionto the Dine-Seiberg problem. We have noted that that string theorycontains many p-form gauge fields. On a compact manifold, the integral ofa field strength F p over a p-cycle is quantized, because of the DNT quantizationcondition. Thus, we can look for solutions of the low energy SUGRAfield equations parametrized by integer values of all of these fluxes. Thiswas proposed in 40 . Bousso and Polchinski 41 pointed out that for Calabi-Yau 3-folds with large b 3 (∼ 100), this could lead to an enormous numberof solutions, of order N b3 with N a large integer. They pointed out thatthis could be used to implement an anthropic explanation of the value ofthe cosmological constant, along lines first suggested in 45 (see also 46 ). Thebasic idea was that each generic choice of fluxes would stabilize the moduliand correspond to a new minimum of the effective potential, with a differentenergy density. Among this huge choice of minima, there are likely to bemany (because the number of allowed flux configurations is exponentiallylarger than 10 123 ) that satisfy Weinberg’s criterion for galaxy formation 44 .Galaxies, and life of our type, could only exist in those.Giddings, Kachru and Polchinski 42 showed that in IIB supergravitycompactifications on CY 3-folds, in the presence of D-branes and orientifolds,all complex structure moduli and the dilaton were stabilized atthe classical level. Kachru, Kallosh, Linde and Trivedi 43 argued that theremaining moduli could be stabilized by non-perturbative effects in lowenergy field theory/D-brane physics, and that the inverse string couplingand CY-3 size were large at the stable minima - so that the calculationswere self consistent in effective field theory. They also showed how to findmeta-stable de Sitter minima, using the same techniques. A large numberof refinements of these calculations have appeared.These considerations can be criticized at both a fundamental and aphenomenological level. String theory concepts, such as D-branes and orientifoldsare known to make sense only when the non-compact co-dimensionof the branes is larger than 1. Here they are being used for space-filling