Lectures on Nongeometric Flux Compactifications

Abstract

These notes present a pedagogical review of nongeometric flux compactifications. We begin by reviewing well-known geometric flux compactifications in Type II string theory, and argue that one must include nongeometric "fluxes" in order to have a superpotential which is invariant under T-duality. Additionally, we discuss some elementary aspects of the worldsheet description of nongeometric backgrounds. This review is based on lectures given at the 2007 RTN Winter School at CERN.

31 pages, JHEP3

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• β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework
• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions
• Non-associative Deformations of Geometry in Double Field Theory
• Slow-Roll Inflation in Non-geometric Flux Compactification
• E7(7) formulation of N=2 backgrounds
• More stable dS vacua from S-dual non-geometric fluxes
• Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry
• Phenomenology of 10^32 Dark Sectors
• On Type IIB moduli stabilization and N = 4, 8 supergravities
• Conformal chiral boson models on twisted doubled tori and non-geometric string vacua
• Spontaneous N=2 to N=1 Supersymmetry Breaking in Supergravity and Type II String Theory
• The Revival of (0,2) Linear Sigma Models
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• Non-geometric flux vacua, S-duality and algebraic geometry
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• How many fluxes fit in an EFT?
• Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
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• Weaving the Exotic Web
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• Heterotic compactifications on SU(2)-structure backgrounds
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• Type II compactifications on manifolds with SU(2) x SU(2) structure
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• Backreacted T-folds and non-geometric regions in configuration space
• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
• The N=4 effective action of type IIA supergravity compactified on SU(2)-structure manifolds
• Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
• Symplectic formulation of the type IIA nongeometric scalar potential
• Order ${\alpha }^{\prime }$ heterotic domain walls with warped nearly Kähler geometry
• Type IIA orientifold compactification on SU(2)-structure manifolds
• Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds
• On stable type IIA de-Sitter vacua with geometric flux
• Nongeometric background arising in the solution of Neumann boundary conditions
• On Missing Bianchi Identities in Cohomology Formulation
• Left-invariant Einstein metrics on $S^3\times S^3$
• Degenerations of K3, Orientifolds and Exotic Branes
• M-theory on non-Kähler manifolds
• Lie algebroids, non-associative structures and non-geometric fluxes
• On the limitations of non-geometric fluxes to realize dS vacua
• Geometric U-folds in four dimensions
• The Generalised Geometry of Type II Non-Geometric Fluxes Under T and S Dualities
• Hypermoduli Stabilization, Flux Attractors, and Generating Functions
• Generalized Geometry and Partial Supersymmetry Breaking
• Dimensional Reductions of DFT and Mirror Symmetry for Calabi-Yau Three-folds and $K3\times T^2$
• Minkowski vacuum transitions in (non-geometric) flux compactifications