F-theory is a branch of string theory developed by Cumrun Vafa. [1] 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".[2]

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 \( {\displaystyle 10^{272,000}} \)elements or so, is dominated by F-theory compactifications on Calabi–Yau four-folds.[3] There are about \( 10^{15} \) of those solutions consistent with the Standard Model of particle physics. [4]

New models of Grand Unified Theory have recently been developed using F-theory.[5]
Extra time dimensions

F-theory, as it has metric signature (11,1), as needed for the Euclidean interpretation of the compactification spaces (e.g. the four-folds), is not a "two-time" theory of physics.

However, the signature of the two additional dimensions is somewhat ambiguous due to their infinitesimal character. For example, the supersymmetry of F-theory on a flat background corresponds to type IIB (i.e. (2,0)) supersymmetry with 32 real supercharges which may be interpreted as the dimensional reduction of the chiral real 12-dimensional supersymmetry if its spacetime signature is (10,2). In (11,1) dimensions, the minimum number of components would be 64. The superfield C being a cocycle of the ordinary 4-differential cohomology on Calabi-Yau varieties of moduli spaces of line bundles which under decomposition into various cup product associated with a divisor of the CY4, yields intermediate Jacobians and Artin-Mazur formal groups of degrees of maximum three (0,1,2).
See also



Vafa, Cumrun (1996). "Evidence for F-theory". Nuclear Physics B. 469 (3): 403–415. arXiv:hep-th/9602022. doi:10.1016/0550-3213(96)00172-1.
Michio Kaku: The Universe Is a Symphony of Vibrating Strings - YouTube
Taylor, Washington; Wang, Yi-Nan (2015). "The F-theory geometry with most flux vacua". Journal of High Energy Physics. 2015 (12): 164. arXiv:1511.03209. Bibcode:2015JHEP...12..164T. doi:10.1007/JHEP12(2015)164.
[1903.00009] A Quadrillion Standard Models from F-theory
Heckman, Jonathan J. (2010). "Particle Physics Implications of F-Theory". Annual Review of Nuclear and Particle Science. 60: 237–265. arXiv:1001.0577. doi:10.1146/annurev.nucl.012809.104532.

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