Uber-naturalness: unexpectedly light scalars from supersymmetric extra dimensions

TL;DR

The paper addresses the problem of keeping non-Goldstone scalars light in theories with extra dimensions and supersymmetry, challenging the view that quantum effects must lift them near the KK or gravitino scale. It exploits large-volume Type IIB string compactifications to relate the gravity, string, and compactification scales via $M_p : M_g : M_{KK} : M_{3/2} = 1 : V^{-1/2} : V^{-2/3} : V^{-1}$, and shows the leading radiative corrections to the light volume modulus are suppressed as $ig|rac{\delta m}{M_p}\big| \\sim V^{-5/3}$, keeping $M_V \\sim M_p / V^{3/2}$ parametrically lighter than both $M_{KK}$ and $M_{3/2}$. This robustness arises from SUSY-related cancellations and the suppressed couplings of moduli to visible-sector matter, yielding an über-natural hierarchy where gravity-scale suppression protects light scalars. The work also outlines LV scenario variants with differing volume $\mathcal{V}$ that realize phenomenologically interesting regimes, such as TeV-scale strings or very light gravitini, while discussing cosmological and inflationary implications and potential experimental signals. Overall, it provides a concrete UV-complete context in which light scalars are natural, guiding future model-building and phenomenology in string-inspired extra-dimensional frameworks.

Abstract

Standard lore asserts that quantum effects generically forbid the occurrence of light (non-pseudo-Goldstone) scalars having masses smaller than the Kaluza Klein scale, M_KK, in extra-dimensional models, or the gravitino mass, M_3/2, in supersymmetric situations. We argue that a hidden assumption underlies this lore: that the scale of gravitational physics, M_g, (e.g. the string scale, M_s, in string theory) is of order the Planck mass, M_p = 10^18 GeV. We explore sensitivity to this assumption using the spectrum of masses arising within the specific framework of large-volume string compactifications, for which the ultraviolet completion at the gravity scale is explicitly known to be a Type IIB string theory. In such models the separation between M_g and M_p is parameterized by the (large) size of the extra dimensional volume, V (in string units), according to M_p: M_g: M_KK: M_3/2 = 1: V^{-1/2}: V^{-2/3}: V^{-1}. We find that the generic size of quantum corrections to masses is of the order of M_KK M_3/2 / M_p ~ M_p / V^{5/3}. The mass of the lighest modulus (corresponding to the extra-dimensional volume) which at the classical level is M_V ~ M_p/V^{3/2} << M_3/2 << M_KK is thus stable against quantum corrections. This is possible because the couplings of this modulus to other forms of matter in the low-energy theory are generically weaker than gravitational strength (something that is also usually thought not to occur according to standard lore). We discuss some phenomenological and cosmological implications of this observation.