F-theory

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 ${\displaystyle 10^{15}}$  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]

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

• Dilaton
• Axion
• M-theory