Über-naturalness: unexpectedly light scalars from supersymmetric extra dimensions

Standard lore asserts that quantum effects generically forbid the occurrence of light (non-pseudo-Goldstone) scalars having masses smaller than the Kaluza Klein scale, MKK, in extra-dimensional models, or the gravitino mass, M3/2, in supersymmetric situations. We argue that a hidden assumption underlies this lore: that the scale of gravitational physics, Mg, (e.g the string scale, Ms, in string theory) is of order the Planck mass, $$ {M_p} = \sqrt {{8\pi G}} \simeq {10^{18}} $$ 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 Mg and Mp is parameterized by the (large) size of the extra dimensional volume, $$ \mathcal{V} $$ (in string units), according to Mp: Mg: MKK: M3/2 ∝ 1: $$ {\mathcal{V}^{ - {{1} \left/ {2} \right.}}}:{\mathcal{V}^{ - {{2} \left/ {3} \right.}}}:{\mathcal{V}^{ - 1}} $$. We find that the generic size of quantum corrections to masses is of the order of MKKM3/2/Mp ≃ $$ {{{{M_p}}} \left/ {{{\mathcal{V}^{{{5} \left/ {3} \right.}}}}} \right.} $$. The mass of the lighest modulus (corresponding to the extra-dimensional volume) which at the classical level is MV ≃ $$ {{{{M_p}}} \left/ {{{\mathcal{V}^{{{3} \left/ {2} \right.}}}}} \right.} $$ ≪M3/2 ≪MKK 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.