Six-dimensional supergravity braneworlds and the cosmological constant

We review the lore of effective field theories as a background to hierarchy problems in general and the cosmological constant problem in particular. We outline some of the attempted four-dimensional solutions to the cosmological con stant problem and conclude that ones based upon the usual assumptions of four-dimensiona lfield theory typically do not work. We argue that one way to relax the assumptions is to seek solutions to the cosmological constant problem which rely on the presence of extra dimensions. We explicitly exhibit that standard compactification techniques fail to solve the cosmological constant problem because they reduce the problem to a four-dimensional one.We argue that brave-world models may be helpful in solving the cosmological constant problem because standard model loops contribute to the tension and not to the vacuum energy directly, and can fulfill our stated aim of constructing a model which uses the extra dimensions to mitigate the cosmological constant problem. We identify necessary (not sufficient) properties a theory must possess to successfully use this observation. These properties are: a scaling symmetry encoded in a dilaton-like scalar, and bulk supersymmetry.We therefore investigate supersymmetric six-dimensional brave-world models. Our models are imbedded within a 6D supergravity that has many of the features of realistic string models. We explicitly show that the compactification of the 6D theory has many of the same features as string compactifications, including flat four-dimensional space, chiral fermions, rnoduli, moduli-stabilisation using fluxes, and gluino condensation. We show that by calculating the non-perturbative correction to the superpotential and loop-corrections to the Kahler function that a meta-stable deSitter vacuum can be found. The vacuum energy can be tuned to be ∼ 10-6 M4Planck .We find that all solutions of the supergravity equations of motion, under a symmetry ansatz, have flat braves. This implies that this property is independent of some of the details of the braves, such as their tensions. The source of the branes' flatness is the required classical scaling symmetry of the action.We consider whether this class of models may provide a solution to the cosmological constant problem within the large extra dimensions scenario, in which the radius r ∼ 0.1mm, and in which the standard-model fields are trapped on a 3-brave. We conclude that it may be possible to produce naturally a cosmological constant that is of order r -4 ∼ (10-3eV)4 due to loops because the supersymmetry-breaking scale in the bulk is MSUSY ∼ r-1; although there remains a great deal of work to be done. We comment on recent extensions to cosmological backgrounds.Further work within these models is outlined, including higher-dimensional models, use of effective field-theory techniques in theories with sharp boundaries, and the treatment of quantum corrections