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Preprints Archive: Abstract of IC2010013 (2010)

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Uber-naturalness: Unexpectedly light scalars from supersymmetric extra dimensions

by C.P. Burgess, Anshuman Maharana and F. Quevedo

Document info: Pages 31, Figures 0.

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, $M_g$, ({\it e.g} the string scale, $M_s$, 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 $M_g$ and $M_p$ is parameterized by the (large) size of the extra dimensional volume, $\V$ (in string units), according to $M_p: M_g: M_\KK: M_{3/2} \propto 1: \V^{-1/2}: \V^{-2/3}: \V^{-1}$. We find that the generic size of quantum corrections to masses is of the order of $M_\KK M_{{3/2}} / M_p \simeq M_p/\V^{5/3}$. The mass of the lighest modulus (corresponding to the extra-dimensional volume) which at the classical level is $M_\ssV \simeq M_p/\V^{3/2} \ll M_{3/2} \ll M_\KK$ 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 {\em 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.

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