At large complex structure in F-theory, the F-term potential simplifies to V = Z^{AB} ρ_A ρ_B, yielding two families of flux vacua with all complex structure moduli fixed, one with bounded saxion vevs and one with unbounded vevs where N_flux factors into two integers.
Denef, Lectures on constructing string vacua, Les Houches87, 483 (2008), arXiv:0803.1194 [hep-th]
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abstract
These lectures give a detailed introduction to constructing and analyzing string vacua suitable for phenomenological model building, with particular emphasis on F-theory flux vacua. Topics include (1) general challenges and overview of some proposed scenarios, (2) an extensive introduction to F-theory and its relation to M-theory and perturbative IIB string theory, (3) F-theory flux vacua and moduli stabilization scenarios, (4) a practical geometrical toolkit for constructing string vacua from scratch, (5) statistics of flux vacua, and (6) explicit models.
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In a wafer-modified Bousso-Polchinski model, 99.95% of the 532 million Calabi-Yau fourfold configurations in the Schöller-Skarke database allow vacuum energy spacings of 10^{-120} or smaller, with membrane nucleation transitions dominated by giant flux leaps under thin-wall approximations.
QCD axions constrain F-theory base threefolds to have rigid or flux-rigidified divisors, yielding typical axion masses around 10^{-9} eV and decay constants near 10^{15} GeV in allowed regions.
String theory imposes constraints on dark energy but permits various construction attempts for de Sitter vacua and single-field exponential quintessence models despite obstructions.
Lecture notes providing a technical introduction to naturalness problems and the string theory landscape for graduate students.
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F-theory flux vacua at large complex structure
At large complex structure in F-theory, the F-term potential simplifies to V = Z^{AB} ρ_A ρ_B, yielding two families of flux vacua with all complex structure moduli fixed, one with bounded saxion vevs and one with unbounded vevs where N_flux factors into two integers.
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Small Vacuum Energy and Tunneling in a Modified Bousso-Polchinski Model
In a wafer-modified Bousso-Polchinski model, 99.95% of the 532 million Calabi-Yau fourfold configurations in the Schöller-Skarke database allow vacuum energy spacings of 10^{-120} or smaller, with membrane nucleation transitions dominated by giant flux leaps under thin-wall approximations.
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Constraining F-theory Model Building with QCD Axions
QCD axions constrain F-theory base threefolds to have rigid or flux-rigidified divisors, yielding typical axion masses around 10^{-9} eV and decay constants near 10^{15} GeV in allowed regions.
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Dark energy from string theory: an introductory review
String theory imposes constraints on dark energy but permits various construction attempts for de Sitter vacua and single-field exponential quintessence models despite obstructions.
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Lectures on Naturalness, String Landscape and Multiverse
Lecture notes providing a technical introduction to naturalness problems and the string theory landscape for graduate students.