Dilaton
Encyclopedia
In particle physics
, a dilaton is a hypothetical particle. It also appears in Kaluza-Klein theory's compactification
s of extra dimension
s when the volume of the compactified dimensions vary.
It is a particle of a scalar field Φ; a scalar field that always comes with gravity. In standard general relativity
, Newton's constant, or equivalently, the Planck mass is always constant. If we "promote" this constant to a dynamical field, what we would get is the dilaton.
So, in Kaluza-Klein theories, after dimensional reduction, the effective Planck mass varies as some power of the volume of compactified space. This is why volume can turn out as a dilaton in the lower dimensional effective theory
.
Although string theory naturally incorporates Kaluza–Klein theory
(which first introduced the dilaton), perturbative string theories, such as type I string theory
, type II string theory
and heterotic string
theory, already contain the dilaton in the maximal number of 10 dimensions. However, on the other hand, M-theory
in 11 dimensions does not include the dilaton in its spectrum unless it is compactified
. In fact, the dilaton in type IIA string theory is actually the radion
of M-theory compactified over a circle, while the dilaton in string theory is the radion for the Hořava–Witten model. (For more on the M-theory origin of the dilaton, see http://arxiv.org/abs/hep-th/0601141.)
In string theory
, there is also a dilaton in the worldsheet CFT. The exponential
of its vacuum expectation value
determines the coupling constant
g, as for compact worldsheets by the Gauss-Bonnet theorem and the Euler characteristic
, where g is the genus that counts the number of handles and thus the number of loops or string interactions described by a specific worldsheet.
Therefore the coupling constant is a dynamical variable in string theory, unlike the case of quantum field theory
where it is constant. As long as supersymmetry is unbroken, such scalar fields can take arbitrary values (they are moduli
). However, supersymmetry breaking
usually creates a potential energy
for the scalar fields and the scalar fields localize near a minimum whose position should in principle be calculable in string theory.
The dilaton acts like a Brans–Dicke scalar, with the effective Planck scale
depending upon both the string scale and the dilaton field.
In supersymmetry, the superpartner
of the dilaton is called the dilatino, and the dilaton combines with the axion
to form a complex scalar field.
.
This is more general than Brans–Dicke in that we have a dilaton potential.
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, a dilaton is a hypothetical particle. It also appears in Kaluza-Klein theory's compactification
Compactification
Compactification may refer to:* Compactification , making a topological space compact* Compactification , the "curling up" of extra dimensions in string theory* Compaction...
s of extra dimension
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
s when the volume of the compactified dimensions vary.
It is a particle of a scalar field Φ; a scalar field that always comes with gravity. In standard general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, Newton's constant, or equivalently, the Planck mass is always constant. If we "promote" this constant to a dynamical field, what we would get is the dilaton.
So, in Kaluza-Klein theories, after dimensional reduction, the effective Planck mass varies as some power of the volume of compactified space. This is why volume can turn out as a dilaton in the lower dimensional effective theory
Effective theory
-Effective Theory:An Effective Theory is a theory based on reasonable assumption, if not actual evidence, for the purpose of moving on in an area of study. An effective theory provides a framework to explain certain effects, without the claim that the theory correctly models the underlying ...
.
Although string theory naturally incorporates Kaluza–Klein theory
Kaluza–Klein theory
In physics, Kaluza–Klein theory is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. The theory was first published in 1921. It was proposed by the mathematician Theodor Kaluza who extended general relativity to a five-dimensional spacetime...
(which first introduced the dilaton), perturbative string theories, such as type I string theory
Type I string theory
In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. It is the only one whose strings are unoriented and which contains not only closed strings, but also open strings.The classic 1976 work of Ferdinando Gliozzi, Joel Scherk and...
, type II string theory
Type II string theory
In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. These account for two of the five consistent superstring theories in ten dimensions. Both theories have the maximal amount of supersymmetry — namely 32 supercharges...
and heterotic string
Heterotic string
In physics, a heterotic string is a peculiar mixture of the bosonic string and the superstring...
theory, already contain the dilaton in the maximal number of 10 dimensions. However, on the other hand, M-theory
M-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...
in 11 dimensions does not include the dilaton in its spectrum unless it is compactified
Compactification
Compactification may refer to:* Compactification , making a topological space compact* Compactification , the "curling up" of extra dimensions in string theory* Compaction...
. In fact, the dilaton in type IIA string theory is actually the radion
Radion
Radion may refer to:*Radion , a scalar field in quantum field theory in spacetimes with additional dimensions*A DC comics villain...
of M-theory compactified over a circle, while the dilaton in string theory is the radion for the Hořava–Witten model. (For more on the M-theory origin of the dilaton, see http://arxiv.org/abs/hep-th/0601141.)
In string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
, there is also a dilaton in the worldsheet CFT. The exponential
Exponential function
In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
of its vacuum expectation value
Vacuum expectation value
In quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...
determines the coupling constant
Coupling constant
In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part...
g, as for compact worldsheets by the Gauss-Bonnet theorem and the Euler characteristic
Euler characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent...
, where g is the genus that counts the number of handles and thus the number of loops or string interactions described by a specific worldsheet.
Therefore the coupling constant is a dynamical variable in string theory, unlike the case of quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
where it is constant. As long as supersymmetry is unbroken, such scalar fields can take arbitrary values (they are moduli
Moduli space
In algebraic geometry, a moduli space is a geometric space whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects...
). However, supersymmetry breaking
Supersymmetry breaking
In particle physics, supersymmetry breaking is the process to obtain a seemingly non-supersymmetric physics from a supersymmetric theory which is a necessary step to reconcile supersymmetry with actual experiments. It is an example of spontaneous symmetry breaking...
usually creates a potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...
for the scalar fields and the scalar fields localize near a minimum whose position should in principle be calculable in string theory.
The dilaton acts like a Brans–Dicke scalar, with the effective Planck scale
Planck scale
In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1019 GeV at which quantum effects of gravity become strong...
depending upon both the string scale and the dilaton field.
In supersymmetry, the superpartner
Superpartner
In particle physics, a superpartner is a hypothetical elementary particle. Supersymmetry is one of the synergistic theories in current high-energy physics which predicts the existence of these "shadow" particles....
of the dilaton is called the dilatino, and the dilaton combines with the axion
Axion
The axion is a hypothetical elementary particle postulated by the Peccei-Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics...
to form a complex scalar field.
Dilaton action
The dilaton-gravity action is.This is more general than Brans–Dicke in that we have a dilaton potential.