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

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

2006-12-04

arxiv.org/abs/hep-th/0612023v3

JHEP 0703:095,2007

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/1126-6708/2007/03/095

I discuss some aspects of the moduli space of hyper-K{\"a}hler four-fold compactifications of type II and ${\cal M}$- 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 ${\cal M}$-theory) must be turned on, and we show that they give rise to vacua with ${\cal N}=2$ or ${\cal N}=3$ supersymmetry upon turning on appropriate fluxes. An interesting subtlety involving the symmetric product limit $S^2(K3)$ is pointed out.

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