Critical points and supersymmetric vacua, III: String/M models

Details Critical points and supersymmetric vacua, III: String/M models Critical points and supersymmetric vacua, III: String/M models

2005-06-07

arxiv.org/abs/math-ph/0506015v4

Commun.Math.Phys.265:617-671,2006

Physics

Mathematical Physics

Final revision for publication in Commun. Math. Phys. Minor corrections and editorial changes

Scientific paper

10.1007/s00220-006-0003-7

A fundamental problem in contemporary string/M theory is to count the number of inequivalent vacua satisfying constraints in a string theory model. This article contains the first rigorous results on the number and distribution of supersymmetric vacua of type IIb string theories compactified on a Calabi-Yau 3-fold $X$ with flux. In particular, complete proofs of the counting formulas in Ashok-Douglas and Denef-Douglas are given, together with van der Corput style remainder estimates. We also give evidence that the number of vacua satisfying the tadpole constraint in regions of bounded curvature in moduli space is of exponential growth in $b_3(X)$.

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