String theory


Fundamental objects


Perturbative theory


Nonperturbative results


Phenomenology


Mathematics






Ftheory is a branch of string theory developed by Cumrun Vafa.^{[1]} The new vacua described by Ftheory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in the form of Ftheory compactified on elliptically fibered Calabi–Yau fourfolds. The letter "F" supposedly stands for "Father".^{[2]}
Contents

Compactifications 1

Phenomenology 2

Extra time dimensions 3

See also 4

References 5
Compactifications
Ftheory is formally a 12dimensional theory, but the only way to obtain an acceptable background is to compactify this theory on a twotorus. By doing so, one obtains type IIB superstring theory in 10 dimensions. The SL(2,Z) Sduality symmetry of the resulting type IIB string theory is manifest because it arises as the group of large diffeomorphisms of the twodimensional torus.
More generally, one can compactify Ftheory on an elliptically fibered manifold (elliptic fibration), i.e. a fiber bundle whose fiber is a twodimensional torus (also called an elliptic curve). For example, a subclass of the K3 manifolds is elliptically fibered, and Ftheory on a K3 manifold is dual to heterotic string theory on a twotorus. (Eight dimensions are large.)Also, the modules of those theories should be equal.
The wellknown large number of semirealistic solutions to string theory referred to as the string theory landscape, with 10^{500} elements or so, is dominated by Ftheory compactifications on Calabi–Yau fourfolds.
Phenomenology
New models of unification of the fundamental forces have recently been developed using Ftheory.^{[3]}
Ftheory, as it has metric signature (11,1), as needed for the Euclidean interpretation of the compactification spaces (e.g. the fourfolds), is not a "twotime" theory of physics.
However, the signature of the two additional dimensions is somewhat ambiguous due to their infinitesimal character. For example, the supersymmetry of Ftheory 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 12dimensional 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 RamondRamond and the RR which, by decomposition over bundles on CY4, gives intermediate Jacobians and ArthurMazor groups.
See also
References

^ Cumrun Vafa. "Evidence for Ftheory." Nucl.Phys. B469: 403418,1996 DOI:10.1016/05503213(96)001721. arXiv: hepth/9602022

^ Michio Kaku: The Universe Is a Symphony of Vibrating Strings  YouTube

^ [1001.0577] Particle Physics Implications of Ftheory
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