F-theory is a branch of string theory developed by 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]


  • Compactifications 1
  • Phenomenology 2
  • Extra time dimensions 3
  • See also 4
  • References 5


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. (Eight dimensions are large.)Also, the modules of those theories should be equal.

The well-known large number of semirealistic solutions to string theory referred to as the string theory landscape, with 10^{500} elements or so, is dominated by F-theory compactifications on Calabi–Yau four-folds.


New models of unification of the fundamental forces have recently been developed using F-theory.[3]

Extra time dimensions

F-theory, as it has metric signature (11,1), as needed for the Euclidean interpretation of the compactification spaces (e.g. the four-folds), is not a "two-time" theory of physics.

However, the signature of the two additional dimensions is somewhat ambiguous due to their infinitesimal character. For example, the supersymmetry of F-theory on a flat background corresponds to type IIB (i.e. (2,0)) supersymmetry with 32 real supercharges which may be interpreted as the dimensional reduction of the chiral real 12-dimensional supersymmetry if its spacetime signature is (10,2). In (11,1) dimensions, the minimum number of components would be 64.We can have an superfield C that replaces the Ramond-Ramond and the R-R which, by decomposition over bundles on CY4, gives intermediate Jacobians and Arthur-Mazor groups.

See also


  1. ^ Cumrun Vafa. "Evidence for F-theory." Nucl.Phys. B469: 403-418,1996 DOI:10.1016/0550-3213(96)00172-1. arXiv: hep-th/9602022
  2. ^ Michio Kaku: The Universe Is a Symphony of Vibrating Strings - YouTube
  3. ^ [1001.0577] Particle Physics Implications of F-theory