F-theory

Compactifications

Main article: Compactification (physics)

F-theory is formally a 12-dimensional theory, but the only way to obtain an acceptable background is to compactify this theory on a two-torus. By doing so, one obtains type IIB superstring theory in 10 dimensions. The SL(2,Z) S-duality symmetry of the resulting type IIB string theory is manifest because it arises as the group of large diffeomorphisms of the two-dimensional torus.

More generally, one can compactify F-theory on an elliptically fibered manifold (elliptic fibration), i.e. a fiber bundle whose fiber is a two-dimensional torus (also called an elliptic curve). For example, a subclass of the K3 manifolds is elliptically fibered, and F-theory on a K3 manifold is dual to heterotic string theory on a two-torus. Also, the moduli spaces of those theories should be isomorphic.

The large number of semirealistic solutions to string theory referred to as the string theory landscape, with 10^{272,000} elements or so, is dominated by F-theory compactifications on Calabi–Yau four-folds. There are at least 10^{15} of those solutions consistent with the Standard Model of particle physics.

Phenomenology

New models of Grand Unified Theory have recently been developed using F-theory.

Extra time dimension

F-theory has the metric signature (10,2), which means that it includes a second time dimension.

References

References

1. (1996). "Evidence for F-theory". Nuclear Physics B.
2. [https://www.youtube.com/watch?v=fW6JFKgbAF4&feature=relmfu Michio Kaku: The Universe Is a Symphony of Vibrating Strings – YouTube]
3. (2015). "The F-theory geometry with most flux vacua". Journal of High Energy Physics.
4. [https://arxiv.org/abs/1903.00009 [1903.00009] A Quadrillion Standard Models from F-theory]
5. (2010). "Particle Physics Implications of F-Theory". [[Annual Review of Nuclear and Particle Science]].
6. Penrose, Roger. (2004). ''The Road to Reality''. Jonathan Cape. Page 915. (Penrose cites Vafa. (1996) and also Bars, I. (2000). "Survey of Two-Time Physics". https://arxiv.org/abs/hep-th/0008164 )