Anisotropic modulus stabilisation: strings at LHC scales with micron-sized extra dimensions
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We construct flux-stabilised IIB compactifications whose extra dimensions
(EDs) have very different sizes, and use these to describe several vacua with a
TeV string scale. Because we can access regimes where 2 dimensions are
hierarchically larger than the other 4, we find examples where 2 dimensions are
micron-sized while the other 4 are at the weak scale in addition to standard
examples with all 6 EDs equally large. Besides providing UV completeness, the
phenomenology of these models is richer than vanilla large-dimensional models
in several ways: (i) they are supersymmetric, with SUSY broken at sub-eV scales
in the bulk but only nonlinearly realised in the SM sector, leading to no MSSM
superpartners and many more bulk missing-energy channels, as in supersymmetric
large extra dimensions (SLED); (ii) small cycles in the complicated
extra-dimensional geometry allow some KK states to reside at TeV scales even if
all 6 EDs are much larger; (iii) a rich spectrum of string and KK states at TeV
scales; and (iv) an equally rich spectrum of light moduli having unusually
small (but technically natural) masses, with potentially interesting
implications for cosmology and astrophysics that nonetheless evade new-force
constraints. The hierarchy problem is solved because the extra-dimensional
volume is naturally stabilised at exponentially large values: the EDs are CY
geometries with a 4D K3 or T^4-fibration over a 2D base, with moduli stabilised
within the LARGE-Volume scenario. The new technical step is the use of
poly-instanton corrections to the superpotential (which, unlike for simpler
models, are likely to be present on K3 or T^4-fibered CY compactifications) to
obtain a large hierarchy between the sizes of different dimensions. For several
scenarios we identify the low-energy spectrum and briefly discuss some of their
astrophysical, cosmological and phenomenological implications.