Über-naturalness: unexpectedly light scalars from supersymmetric extra dimensions
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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.