Anisotropic Modulus Stabilisation: Strings at LHC Scales with Micron-sized Extra Dimensions

TL;DR

This paper constructs flux-stabilized IIB string compactifications with extra dimensions of vastly different sizes, including micron-sized and TeV-scale dimensions, leading to rich phenomenology and solutions to the hierarchy problem.

Contribution

It introduces a new class of flux-stabilized compactifications with anisotropic extra dimensions, utilizing poly-instanton corrections to achieve large hierarchies and diverse phenomenological features.

Findings

Extra dimensions include micron-sized and TeV-scale sizes.

Rich spectrum of string and KK states at TeV scales.

Light moduli with small masses potentially impacting cosmology.

Abstract

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.