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Register a new userStatistical Distribution of the Vacuum Energy Density in Racetrack Kahler Uplift Models in String Theory
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We study a racetrack model in the presence of the leading alpha-correction in flux compactification in Type IIB string theory, for the purpose of getting conceivable de-Sitter vacua in the large compactified volume approximation. Unlike the Kahler Uplift model studied previously, the alpha-correction is more controllable for the meta-stable de-Sitter vacua in the racetrack case since the constraint on the compactified volume size is very much relaxed. We find that the vacuum energy density Lambda for de-Sitter vacua approaches zero exponentially as the volume grows. We also analyze properties of the probability distribution of Lambda in this class of models. As in other cases studied earlier, the probability distribution again peaks sharply at Lambda=0. We also study the Racetrack Kahler Uplift model in the Swiss-Cheese type model.
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As the vacuum state of a quantum field is not an eigenstate of the Hamiltonian density, the vacuum energy density can be represented as a random variable. We present an analytical calculation of the probability distribution of the vacuum energy density for real and complex massless scalar fields in Minkowski space. The obtained probability distributions are broad and the vacuum expectation value of the Hamiltonian density is not fully representative of the vacuum energy density.
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