Presents a seam-graded recursive algebraic method that converts the closed string tachyon vacuum equation into a sequence of matrix inversions in the zero-momentum Lorentz-scalar sector.
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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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Recursive-algebraic solution of the closed string tachyon vacuum equation
Presents a seam-graded recursive algebraic method that converts the closed string tachyon vacuum equation into a sequence of matrix inversions in the zero-momentum Lorentz-scalar sector.
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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.