The KK-compactification of F-theory on Spin(7)-manifolds to 4d. Differs subtly from F-theory on CY4.
Related by T-duality to 3d M-theory on Spin(7)-manifolds
What has been called Witten's dark fantasy in Heckmann-Lawrie-Lin-Zoccarato 19, Section 8 is an argument, going back to Witten 95a, Witten 95b, Sec. 3, Witten 00, p. 7 for the existence of non-perturbative non-supersymmetric 4d string vacua/string phenomenology with fundamentally vanishing cosmological constant (“dark energy”).
The original idea was formulated in terms of 3d M-theory on 8-manifolds decompactified at strong coupling to 4d via duality between M-theory and type IIA string theory (recall the super 2-brane in 4d).
Based on the observation of Vafa 96, Section 4.3 that the argument should have a natural realization in 4d F-theory on Spin(7)-manifolds (T-dual to the previous perspective), a detailed construction was finally laid out in Bonetti-Grimm-Pugh 13, Heckmann-Lawrie-Lin-Zoccarato1 18, Heckman-Lawrie-Lin-Sakstein-Zoccarato 19.
The key technical point is the claim that a careful analysis of D=4 N=1 supergravity obtained after KK-compactification of F-theory on Spin(7)-manifolds T-dual to M-theory on Spin(7)-manifolds reveals a “1/2 supersymmetry” where
the vacuum state is supersymmetric and hence has vanishing cosmological constant;
but no finite-energy-excitation of the vacuum appears supersymmetrically,
hence fermions and bosons in the model do not appear in supersymmetric spectra.
(Vafa 96, Sec. 4.3 BGP 13, HLLZ 18, Sec. 4)
On a spin-manifold of dimension 8 a choice of topological Spin(7)-structure is equivalently a choice of cocycle in J-twisted Cohomotopy cohomology theory. This follows (FSS 19, 3.4) from
the standard coset space-structures on the 7-sphere (see here)
the fact that coset spaces $G/H$ are the homotopy fibers of the maps $B H \to B G$ of the corresponding classifying spaces (see here)
F-theory KK-compactified on elliptically fibered complex analytic fiber $\Sigma$
$dim_{\mathbb{C}}(\Sigma)$ | 1 | 2 | 3 | 4 |
---|---|---|---|---|
F-theory | F-theory on CY2 | F-theory on CY3 | F-theory on CY4 |
The concept goes back to
See also:
Mariana Graña, C. S. Shahbazi, Marco Zambon, $Spin(7)$-manifolds in compactifications to four dimensions, JHEP11(2014)046 (arXiv:1405.3698)
Andreas Braun, Sakura Schafer-Nameki, Spin(7)-Manifolds as Generalized Connected Sums and 3d $N=1$ Theories, JHEP06(2018)103 (arXiv:1803.10755)
(generalization of compact twisted connected sum G2-manifolds)
Relating M-theory on Spin(7)-manifolds with F-theory on Spin(7)-manifolds via Higgs bundles:
Already Vafa 96, Section 4.3 mentions the relation to Witten's Dark Fantasy, then developed in
Federico Bonetti, Thomas Grimm, Tom Pugh, Non-Supersymmetric F-Theory Compactifications on $Spin(7)$ Manifolds, JHEP 01 (2014) 112 (arXiv:1307.5858)
Federico Bonetti, Thomas Grimm, Eran Palti, Tom Pugh, F-Theory on $Spin(7)$ Manifolds: Weak-Coupling Limit, JHEP 02 (2014) 076 (arXiv:1309.2287)
Jonathan Heckman, Craig Lawrie, Ling Lin, Gianluca Zoccarato, F-theory and Dark Energy, Fortschritte der Physik (arXiv:1811.01959, doi:10.1002/prop.201900057)
Jonathan Heckman, Craig Lawrie, Ling Lin, Jeremy Sakstein, Gianluca Zoccarato, Pixelated Dark Energy (arXiv:1901.10489)
See also
Tom Pugh, M-theory on $Spin(7)$-manifold duals and their F-theory duals (pdf)
Federico Bonetti, Thomas Grimm, Eran Palti, Tom Pugh, F-Theory on Spin(7) Manifolds: Weak-Coupling Limit, J. High Energ. Phys. (2014) 2014: 76 (arXiv:1309.2287)
Last revised on April 1, 2020 at 03:42:37. See the history of this page for a list of all contributions to it.