Anisotropic modulus stabilisation: strings at LHC scales with micron-sized extra dimensions

We construct flux-stabilised Type IIB string compactifications whose extra dimensions have very different sizes, and use these to describe several types of vacua with a TeV string scale. Because we can access regimes where two dimensions are hierarchically larger than the other four, we find examples where two dimensions are micron-sized while the other four are at the weak scale in addition to more standard examples with all six extra dimensions equally large. Besides providing ultraviolet completeness, the phenomenology of these models is richer than vanilla large-dimensional models in several generic ways: (i) they are supersymmetric, with supersymmetry broken at sub-eV scales in the bulk but only nonlinearly realised in the Standard Model sector, leading to no MSSM superpartners for ordinary particles and many more bulk missing-energy channels, as in supersymmetric large extra dimensions (SLED); (ii) small cycles in the more complicated extra-dimensional geometry allow some KK states to reside at TeV scales even if all six extra dimensions are nominally much larger; (iii) a rich spectrum of string and KK states at TeV scales; and (iv) an equally rich spectrum of very light moduli exist 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 in these models because the extra-dimensional volume is naturally stabilised at exponentially large values: the extra dimensions are Calabi-Yau geometries with a 4D K3 or T4-fibration over a 2D base, with moduli stabilised within the well-established 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 T4-fibered Calabi-Yau 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.