In
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
, F-theory is a branch of
string theory developed by Iranian physicist
Cumrun Vafa
Cumrun Vafa ( fa, کامران وفا ; born 1 August 1960) is an Iranian-American theoretical physicist and the Hollis Professor of Mathematics and Natural Philosophy at Harvard University.
Early life and education
Cumrun Vafa was born in Tehra ...
. 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".
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, one obtains
type IIB superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings.
'Superstring theory' is a shorthand for supersymmetric string t ...
in 10 dimensions. The
SL(2,Z) S-duality
In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theoret ...
symmetry of the resulting type IIB string theory is manifest because it arises as the group of
large diffeomorphism
In mathematics and theoretical physics, a large diffeomorphism is an equivalence class of diffeomorphisms under the equivalence relation where diffeomorphisms that can be continuously connected to each other are in the same equivalence class.
For ...
s of the two-dimensional
torus
In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.
If the axis of revolution does not tou ...
.
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
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...
). 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
The string theory landscape or landscape of vacua refers to the collection of possible false vacua in string theory,The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See M. Douglas, "The ...
, with
elements or so, is dominated by F-theory compactifications on
Calabi–Yau four-folds. There are about
of those solutions consistent with the Standard Model of particle physics.
Phenomenology
New models of
Grand Unified Theory
A Grand Unified Theory (GUT) is a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this ...
have recently been developed using F-theory.
Extra time dimension
F-theory has the
metric signature
In mathematics, the signature of a metric tensor ''g'' (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and ...
(10,2), which includes a
second time dimension.
[Penrose, Roger. (2004). ''The Road to Reality''. Jonathan Cape. Page 915. (Penrose cites Vafa. (1996) and also Bars, I. (2000). "Survey of Two-Time Physics". https://arxiv.org/abs/hep-th/0008164 )]
See also
*
Dilaton
In particle physics, the hypothetical dilaton particle is a particle of a scalar field \varphi that appears in theories with extra dimensions when the volume of the compactified dimensions varies. It appears as a radion in Kaluza–Klein theor ...
*
Axion
*
M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's ...
References
String theory
{{string-theory-stub