Duality in heterotic vacua with four supercharges

Calabi-Yau fourfolds with flux and supersymmetry breaking

“…21 In case χ is divisible by 24 this implies F 4 /2π ∈ H 4 (X, Z). The way we want to ensure this is by demanding that J, ℜ(Ω) and ℑ(Ω) are all integral themselves and by using integral coefficients F,F in the expansion (3.50).…”

“…The compactification without flux was investigated in [21]. 9 The starting point is the eleven-dimensional supergravity with (bosonic) Lagrangian [26] e −1 L (11) = 1 2…”

“…the chiral fields should be those appearing also in the dualized version without vector multiplets, and the scalars from the vector multiplets should obey (2.15). The correct Kähler coordinates in the dualized theory were determined in [21]. In the case without flux, the dualization can be performed explicitly by adding a Lagrange multiplier term…”

“…12 Note that the notation slightly differs from [21] in order to be consistent with the notation of section 2. and eliminating the fields F A µ via their equations of motion. The Kähler structure of the resulting sigma-model becomes manifest when expressed in the coordinates φ i = (Z α ,N I , φ A ), wherê…”

De Sitter string vacua from perturbative Kähler corrections and consistent D-terms

“…In particular, the most pressing issues have been how to stabilize the geometrical moduli of a compactification, and at the same time address the tiny, positive cosmological constant that is inferred from the present-day accelerated expansion of the universe. Recently, the use of closed string background fluxes in string compactifications has been studied in this context [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. Such flux compactifications can stabilize the dilaton and the complex structure moduli in type IIB string theory.…”