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Intheoretical physics,F-theory is a branch ofstring theory developed by Iranian-American physicistCumrun Vafa.[1] The newvacua 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 fiberedCalabi–Yau four-folds. The letter "F" supposedly stands for "Father" in relation to"Mother"-theory.[2]
F-theory is formally a 12-dimensional theory, but the only way to obtain an acceptable background is tocompactify this theory on atwo-torus. By doing so, one obtainstype IIBsuperstring theory in 10 dimensions. TheSL(2,Z)S-duality symmetry of the resulting type IIB string theory is manifest because it arises as the group oflarge diffeomorphisms of the two-dimensionaltorus.
More generally, one can compactify F-theory on an elliptically fiberedmanifold (elliptic fibration), i.e. afiber bundle whose fiber is a two-dimensional torus (also called anelliptic curve). For example, a subclass of theK3 manifolds is elliptically fibered, and F-theory on a K3 manifold is dual toheterotic 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 thestring theory landscape, with elements or so, is dominated by F-theory compactifications onCalabi–Yau four-folds.[3] There are at least of those solutions consistent with the Standard Model of particle physics.[4]
New models ofGrand Unified Theory have recently been developed using F-theory.[5]
F-theory has themetric signature (10,2), which means that it includes asecond time dimension.[6]
