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

SUSY Breaking and Moduli Stabilization from Fluxes in Gauged 6D Supergravity

We construct the 4D N=1 supergravity which describes the low-energy limit of 6D supergravity compactified on a sphere with a monopole background a la Salam and Sezgin. This provides a simple setting sharing the main properties of realistic string compactifications such as flat 4D spacetime, chiral fermions and N=1 supersymmetry as well as Fayet-Iliopoulos terms induced by the Green-Schwarz mechanism. The matter content of the resulting theory is a supersymmetric SO(3)xU(1) gauge model with two chiral multiplets, S and T. The expectation value of T is fixed by the classical potential, and S describes a flat direction to all orders in perturbation theory. We consider possible perturbative corrections to the Kahler potential in inverse powers of $Re S$ and $Re T$, and find that under certain circumstances, and when taken together with low-energy gaugino condensation, these can lift the degeneracy of the flat direction for $Re S$. The resulting vacuum breaks supersymmetry at moderately low energies in comparison with the compactification scale, with positive cosmological constant. It is argued that the 6D model might itself be obtained from string compactifications, giving rise to realistic string compactifications on non Ricci flat manifolds. Possible phenomenological and cosmological applications are briefly discussed.Comment: 32 pages, 2 figures. Uses JHEP3.cls. References fixed and updated, some minor typos fixed. Corrected minor error concerning Kaluza-Klein scales. Results remain unchange

Enhanced fluctuation-driven neutrino scattering behind supernova shocks

We describe a general formalism for computing scattering rates of weak probes in macroscopic systems, based on a density matrix formalism. We show that weak probes in general scatter off fluctuations in the medium. In the limit that the neutrino wavelength is much larger than the lengthscale of the fluctuations, we show that the scattering rate can be calculated from knowledge of the equation of state of the medium through which the neutrinos travel. Using radial profiles of a post-bounce, shocked supernova core and a well-established equation of state for nuclear matter we compute these scattering rates for various times in the vicinity of the shock. We find that, behind the shock, these correlative effects can enhance neutrino scattering rates by factors of 8 compared to standard calculations which ignore interactions in the nuclear medium. These results may have implications for how efficiently neutrinos can restart a stalled shock, although firm conclusions regarding the ultimate effects of such an enhancement await full hydrodynamic simulations, which are not performed here