Moduli
Calabi-Yau:
Kähler manifold with SU(3) holonomy and vanishing first Chern class (c₁=0). Required for N=1 SUSY in 4D.
Hodge numbers:
h^(1,1) = Kähler moduli (shape of 2-cycles)
h^(2,1) = complex structure moduli
Euler characteristic:
χ = 2(h^(1,1) − h^(2,1))
determines number of generations!
Landscape:
~10⁵⁰⁰ vacua from flux compactification (KKLT).
Kähler manifold with SU(3) holonomy and vanishing first Chern class (c₁=0). Required for N=1 SUSY in 4D.
Hodge numbers:
h^(1,1) = Kähler moduli (shape of 2-cycles)
h^(2,1) = complex structure moduli
Euler characteristic:
χ = 2(h^(1,1) − h^(2,1))
determines number of generations!
Landscape:
~10⁵⁰⁰ vacua from flux compactification (KKLT).