# F-theory

**F-theory**is a branch ofstring theory developed byCumrun Vafa . The new vacua described as F-theory were discovered by Vafa, and it also allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fiberedCalabi-Yau four-folds. The letter "F" stands for "Father" much like the "M" inM-theory is often taken to stand for "Mother".**Compactifications**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, we obtain type IIB

superstring 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 diffeomorphism s of the two-dimensionaltorus .More generally, one can compactify F-theory on an elliptically fibered

manifold (elliptic fibration ), i.e. afiber bundle whose fiber is a two-dimensional torus (also called anelliptic curve ). For example, a subclass of theK3 manifold s is elliptically fibered, and F-theory on a K3 manifold is dual toheterotic string theory on a two-torus. (Eight dimensions are large.)The well-known large number of semirealistic solutions to string theory referred to as

string theory landscape , with $10^\{500\}$ elements or so, is dominated by F-theory compactifications onCalabi-Yau four-fold s.**Extra time dimensions**F-theory, as it has

metric signature (11,1), is not a "two-time" theory of physics.string-theory-stub theory is a partial equation theory only of the branescape.

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