Anisotropic Modulus Stabilisation: Strings at LHC Scales with Micron-sized Extra Dimensions
M. Cicoli, C. P. Burgess, F. Quevedo
TL;DR
This work embeds TeV-scale string phenomenology inside an explicit Type IIB flux-compactification framework with highly anisotropic extra dimensions, stabilising two large dimensions and four small ones via LARGE-Volume-like dynamics. It introduces two stabilization pathways—string-loop corrections in the SH regime and poly-instanton corrections in the LH regime—capable of yielding a base two-cycle of micron size while keeping the fiber four-cycles compact, resulting in $M_s \sim 1$ TeV and ${\cal V} \sim 10^{30}$. The model predicts a rich spectrum of TeV-scale KK and string states, a bulk SUSY breaking scale near $m_{3/2} \sim 10^{-3}$ eV with no MSSM superpartners on the SM brane, and ultralight moduli with suppressed couplings, offering novel cosmological and gravitational tests. It also analyzes SLED-like constraints, brane backreaction issues, and possible collider implications, highlighting the distinctive phenomenology enabled by the UV-complete, anisotropic LVS construction.
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.