The moduli space of hyper-K{ä}hler four-fold compactifications

Abstract

I discuss some aspects of the moduli space of hyper-K{ä}hler four-fold compactifications of type II and $\mathcal{M}$- theories. The dimension of the moduli space of these theories is strictly bounded from above. As an example I study Hilb${}^2(K3)$ and the generalized Kummer variety $K^2(T^4)$. In both cases RR-flux (or $G$-flux in $\mathcal{M}$-theory) must be turned on, and we show that they give rise to vacua with $\mathcal{N}=2$ or $\mathcal{N}=3$ supersymmetry upon turning on appropriate fluxes. An interesting subtlety involving the symmetric product limit $S^2(K3)$ is pointed out.

42 pages, discussion of $\mathcal{N}=3$ supersymmetry preserving fluxes added, acknowledegement added

References in corpus (16)

• Black Hole Attractors and the Topological String
• The String Landscape and the Swampland
• Type IIA Moduli Stabilization
• Generalized structures of N=1 vacua
• Supersymmetric Backgrounds from Generalized Calabi-Yau Manifolds
• The Cosmological Constant and the String Landscape
• String loop corrected hypermultiplet moduli spaces
• Black hole partition functions and duality
• Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry
• TASI/PiTP/ISS Lectures on Moduli and Microphysics
• Hypermultiplets and Topological Strings
• Fixing All Moduli for M-Theory on K3xK3
• Twistors and Black Holes
• Quantum Corrections to the Universal Hypermultiplet and Superspace
• Membrane Instantons and de Sitter Vacua
• M-theory on eight-manifolds revisited: N=1 supersymmetry and generalized Spin(7) structures

Cited by in corpus (1)

• Supersymmetry Constraints and String Theory on K3