Abstract
We identify the underlying symmetry mechanism that suppresses the low-energy effective 4D cosmological constant within 6D supergravity models, leading to results suppressed by powers of the KK scale relative to the much larger masses associated with particles localized on codimension-2 branes. In these models the conditions for unbroken supersymmetry can be satisfied locally everywhere within the extra dimensions, but are obstructed by global conditions like flux quantization or the mutual inconsistency of boundary conditions at the various branes. Consequently quantities forbidden by supersymmetry cannot be nonzero until wavelengths of order the KK scale are integrated out, since only such long wavelength modes see the entire space and so know that supersymmetry breaks. We verify these arguments by extending earlier rugby-ball calculations of one-loop vacuum energies to more general pairs of branes within two warped extra dimensions. The predicted effective 4D vacuum energy density can be of order C (m Mg/4 pi Mp)^4, where Mg (Mp) is the rationalized 6D (4D) Planck scale and m is the heaviest brane-localized particle. Numerically this is C (5.6 x 10^{-5} eV)^4 if we take m = 173 GeV and take Mg as small as possible (10 TeV corresponding to KK size r < 1 micron), consistent with supernova bounds. C is a constant depending on details of the bulk spectrum, which could be ~ 500 for each of hundreds of fields. The value C ~ 6 x 10^6 gives the observed Dark Energy density.
Highlights
Williamsa,b aDepartment of Physics & Astronomy, McMaster University, 1280 Main Street West, Hamilton ON, Canada bPerimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo ON, Canada cAbdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, Trieste 34014, Italy E-mail: cburgess@perimeterinstitute.ca, leo.van.nierop@gmail.com, willimr2@mcmaster.ca Abstract: We identify the underlying symmetry mechanism that suppresses the lowenergy effective 4D cosmological constant within some 6D supergravity models, generically leading to results suppressed by powers of the KK scale, m2KK, relative to the much larger size, m4, associated with mass-m particles localized in these models on codimension-2 branes
Progress has been made on separating these issues within 6D extra-dimensional models [3, 4], with some supersymmetry-breaking effects being naturally at the Kaluza-Klein (KK) scale,2 mKK 1/r, even though this is much smaller than the masses, m, for the non-supersymmetric particle content on branes localized within the extra dimensions
In this paper we have considered the implications of recent calculations of the vacuum energy in the scenario of large supersymmetric extra dimensions
Summary
There are several mechanisms at work that allow the decoupling between the scale, m, of particles on the brane and the scale, mKK, of the energy density observed by cosmology. From this point on the discussion proceeds as above, leading for the same reasons to a vacuum energy that is of order the KK scale It does so because the BPS condition could be satisfied by fixing the value, φ, of a bulk zero mode, and this works well for Tb and Ab because it took place for any value of Tb and Ab. A similar interplay between locally unbroken but globally broken internal symmetries has been found to be useful in extra-dimensional versions of Grand Unified theories [38,39,40,41], and have long been pined for as a potential brane-world mechanism for obtaining a small vacuum energy or scalar mass [42, 43]. Related models arise within 4D theories, such as with ‘deconstructed’ dimensions [44] used to produce phenomenological ‘littlest Higgs’ models addressed to the electroweak hierarchy problems of the Higgs boson [45]
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