Abstract
String theory has no parameter except the string scale, so a dynamically compactified solution to 4 dimensional spacetime should determine both the Planck scale and the cosmological constant Λ. In the racetrack Kähler uplift flux compactification model in Type IIB theory, where the string theory landscape is generated by scanning over discrete values of all the flux parameters, a statistical preference for an exponentially small Λ is found to be natural [1]. Within this framework and matching the median Λ value to the observed Λ, a mass scale m ≃ 100 GeV naturally appears. We explain how the electroweak scale can be identified with this mass scale.
Highlights
For a given set of flux parameters F i, we can solve V (F i, φj) for its meta-stable vacuum solutions via finding the values φj,min(F i) at each solution and determine its vacuum energy density Λ = Λ(F i, φj,min(F i)) = Λ(F i)
In the racetrack Kahler uplift flux compactification model in Type IIB theory, where the string theory landscape is generated by scanning over discrete values of all the flux parameters, a statistical preference for an exponentially small Λ is found to be natural [1]
Taking the median value Λ50 in this racetrack Kahler uplift model to match the observed value, a natural scale emerges, Λ50 10−122 MP4 ⇒ m ∼ 102 GeV. Can this scale m correspond to the electroweak scale? In this paper, we give an explicit string theory scenario to realize this property in a concrete statistical way
Summary
Let us review the racetrack Kahler uplift model studied in ref. [1], with the addition of a Higgs-like field. The two terms in the non-perturbative WNP form the racetrack (and stabilise T [16]) They are given by gaugino condensates with coefficients a = 2π/N1, b = 2π/N2 for SU(N1), SU(N2) gauge symmetry respectively. The model includes the first α -correction (the ξ term) to the Kahler potential to lift the supersymmetric solution to de Sitter space [17, 18]. Λ approaches an exponentially small positive value at the large volume (x → ∞) limit. Using C (2.2), one can show that in this limit, As it might be expected from the exponential terms in (2.8) and (2.7), the bigger the volume modulus, the smaller W0 and Λ have to be in order to find a solution. If we match the observed Λ to Λ10, that is, there is only a 10% probability that Λ has a value smaller or equal to the observed value, we find that m drops by less than one order of magnitude
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