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

Abstract

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 $b_3(X)$.

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

References in corpus (4)

• Landscape, the Scale of SUSY Breaking, and Inflation
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• Persistent Homology and String Vacua
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• Manifolds pinned by a high-dimensional random landscape: Hessian at the global energy minimum
• The Distribution of Vacua in Random Landscape Potentials
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• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Asymptotics and Dimensional Dependence of the Number of Critical Points of Random Holomorphic Sections
• Attractors are not algebraic