nLab F/M-theory on elliptically fibered Calabi-Yau 5-folds

Idea

General

The KK flux compactification of M-theory/F-theory on an elliptically fibered Calabi-Yau variety of (complex) dimension 5 (hence real dimension 10) yields, on the F-theory side, type IIB superstring theory (with some S-duality-related non-perturbative effects included) KK-compactified on Calabi-Yau 4-folds, and hence $D=2$, $\mathcal{N}=(2,0)$ QFTs such as D=2 N=(2,0) SCFT, T-dual, on the M-theory-side, to supersymmetric quantum mechanics (see also: BFSS matrix model and E10).

Related concepts

F-theory KK-compactified on elliptically fibered complex analytic fiber $\Sigma$

$dim_{\mathbb{C}}(\Sigma)$	1	2	3	4	5
	F-theory	F-theory on CY2	F-theory on CY3	F-theory on CY4	F-theory on CY5

KK-compactification of M-theory

• M-theory on a circle

• M-theory on 8-manifolds/on Spin(7)-manifolds

• M-theory on G₂-manifolds

  • G₂-MSSM

• M-theory on Sp(1)-manifolds

• M-theory on hyperbolic manifolds

• heterotic M-theory on ADE-orbifolds

• M-theory on Calabi-Yau manifolds

  • on CY2-folds

  • on CY3-folds

  • on CY4-folds

  • on CY5-folds

References

For M-theory and supersymmetric quantum mechanics:

• Alexander Haupt, Andre Lukas, Kellogg Stelle, M-theory on Calabi-Yau Five-Folds, JHEP 0905:069, 2009 (arXiv:0810.2685)

For F-theory and D=2 N=(2,0) SCFT:

• Sakura Schäfer-Nameki, Timo Weigand, F-theory and 2d (0,2) Theories, J. High Energ. Phys. 2016, 59 (2016) (arXiv:1601.02015)

Survey:

• Sakura Schäfer-Nameki, F-theory and $2d$ $(0,2)$ Theories, 2016 (talk slides pdf)