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 List of natural phenomena, natural phenomena. This is in contrast to experimental p ...
, F-theory is a branch of
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
developed by Iranian-American physicist
Cumrun Vafa. 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" in relation to
"Mother"-theory.
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 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
In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanarity, coplanar with the circle. The main types of toruses inclu ...
.
More generally, one can compactify F-theory on an elliptically fibered
manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a N ...
(
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
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 any Mathematical model, model in particle physics that merges the electromagnetism, electromagnetic, weak interaction, weak, and strong interaction, strong fundamental interaction, forces (the three gauge theory, ...
have recently been developed using F-theory.
Extra time dimension
F-theory has the
metric signature (10,2), which means that it 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 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 theory's compa ...
*
Axion
*
M-theory
In physics, M-theory is a theory that unifies all Consistency, 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 1 ...
References
String theory
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