Editing F-theory

{{short description|Branch of string theory}}
{{more citations needed|date=October 2011}}
{{String theory}}

In [[theoretical physics]], '''F-theory''' is a branch of [[string theory]] developed by Iranian-American physicist [[Cumrun Vafa]].<ref>{{cite journal|title=Evidence for F-theory|date=1996|last1=Vafa|first1=Cumrun|doi=10.1016/0550-3213(96)00172-1|journal=Nuclear Physics B|volume=469|issue=3|pages=403–415|arxiv=hep-th/9602022|s2cid=6511691}}</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 manifold|Calabi–Yau four-folds]]. The letter "F" supposedly stands for "Father" in relation to [[M-theory|"Mother"-theory]].<ref>[https://www.youtube.com/watch?v=fW6JFKgbAF4&feature=relmfu Michio Kaku: The Universe Is a Symphony of Vibrating Strings – YouTube]</ref>

==Compactifications==
{{Main|Compactification (physics)}}

F-theory is formally a 12-dimensional theory, but the only way to obtain an acceptable background is to [[compactification (physics)|compactify]] this theory on a [[torus|two-torus]]. By doing so, one obtains [[type IIB string|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 diffeomorphism]]s 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 manifold]]s 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-fold]]s.<ref>{{cite journal|title=The F-theory geometry with most flux vacua|date=2015|last1=Taylor| first1=Washington|last2=Wang|first2=Yi-Nan|doi=10.1007/JHEP12(2015)164|journal=Journal of High Energy Physics|volume=2015|issue=12|pages=164|arxiv=1511.03209 |bibcode=2015JHEP...12..164T|s2cid=41149049}}</ref> There are about <math>10^{15}</math> of those solutions consistent with the Standard Model of particle physics.<ref>[https://arxiv.org/abs/1903.00009 [1903.00009&#93; A Quadrillion Standard Models from F-theory]</ref>

==Phenomenology==
New models of [[Grand Unified Theory]] have recently been developed using F-theory.<ref>{{cite journal|title=Particle Physics Implications of F-Theory|date=2010|last1=Heckman|first1=Jonathan J.|doi=10.1146/annurev.nucl.012809.104532| doi-access=free|journal=[[Annual Review of Nuclear and Particle Science]]|volume=60|pages=237–265|arxiv=1001.0577}}</ref>

==Extra time dimension==
F-theory has the [[metric signature]] (10,2), which means that it includes a [[multiple time dimensions|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>

==See also==
* [[Dilaton]]
* [[Axion]]
* [[M-theory]]

==References==
{{reflist}}

{{String theory topics |state=collapsed}}

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[[Category:String theory]]


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