paper

On three dimensions as the preferred dimensionality of space via the Brandenberger-Vafa mechanism

arXiv:1212.2115 · doi:10.1103/PhysRevD.88.043527

Abstract

In previous work it was shown that, in accord with the Brandenberger-Vafa mechanism, three is the maximum number of spatial dimensions that can grow large cosmologically from an initial thermal fluctuation. Here we complement that work by considering the possibility of successive fluctuations. Suppose an initial fluctuation causes at least one dimension to grow, and suppose successive fluctuations occur on timescales of order alpha'^{1/2}. If the string coupling is sufficiently large, we show that such fluctuations are likely to push a three-dimensional subspace to large volume where winding modes annihilate. In this setting three is the preferred number of large dimensions. Although encouraging, a more careful study of the dynamics and statistics of fluctuations is needed to assess the likelihood of our assumptions.

20 pages, 4 figures. v2: additional references, various improvements for clarity. v3: more improvements, version to appear in PRD

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