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Short description: Branch of string theory

In theoretical physics, F-theory is a branch of string theory developed by Iranian physicist 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 page: Physics:Compactification

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]\displaystyle{ 10^{272,000} }[/math] elements or so, is dominated by F-theory compactifications on Calabi–Yau four-folds.[3] There are about [math]\displaystyle{ 10^{15} }[/math] 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 dimension

F-theory has the metric signature (10,2), which means that it includes a second time dimension.[6]

See also


  1. Vafa, Cumrun (1996). "Evidence for F-theory". Nuclear Physics B 469 (3): 403–415. doi:10.1016/0550-3213(96)00172-1. 
  2. Michio Kaku: The Universe Is a Symphony of Vibrating Strings - YouTube
  3. Taylor, Washington; Wang, Yi-Nan (2015). "The F-theory geometry with most flux vacua". Journal of High Energy Physics 2015 (12): 164. doi:10.1007/JHEP12(2015)164. Bibcode2015JHEP...12..164T. 
  4. [1903.00009] A Quadrillion Standard Models from F-theory
  5. Heckman, Jonathan J. (2010). "Particle Physics Implications of F-Theory". Annual Review of Nuclear and Particle Science 60: 237–265. doi:10.1146/annurev.nucl.012809.104532. 
  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". )