F-theory
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In theoretical physics, F-theory is a branch of string theory developed by Iranian-American physicist Cumrun Vafa.<ref>Template:Cite journal</ref> The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fibered Calabi–Yau four-folds. The letter "F" supposedly stands for "Father" in relation to "Mother"-theory.<ref>Michio Kaku: The Universe Is a Symphony of Vibrating Strings – YouTube</ref>
CompactificationsEdit
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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 <math>10^{272,000}</math> elements or so, is dominated by F-theory compactifications on Calabi–Yau four-folds.<ref>Template:Cite journal</ref> There are about <math>10^{15}</math> of those solutions consistent with the Standard Model of particle physics.<ref>[1903.00009] A Quadrillion Standard Models from F-theory</ref>
PhenomenologyEdit
New models of Grand Unified Theory have recently been developed using F-theory.<ref>Template:Cite journal</ref>
Extra time dimensionEdit
F-theory has the metric signature (10,2), which means that it includes a second time dimension.<ref>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 )</ref>