Dilaton

In particle physics, the hypothetical dilaton particle is a particle of a scalar field ${\displaystyle \varphi }$ that appears in theories with

${\displaystyle \varphi }$ and the associated particle is the dilaton.

Exposition

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

In string theory, there is also a dilaton in the worldsheet CFT – two-dimensional conformal field theory. The exponential of its vacuum expectation value determines the coupling constant g and the Euler characteristic   χ = 2 − 2g   as ${\textstyle \;{\tfrac {1}{2\pi }}\int R=\chi \;}$ for compact worldsheets by the Gauss–Bonnet theorem, where the genus g counts the number of handles and thus the number of loops or string interactions described by a specific worldsheet.

${\displaystyle g=\exp \left(\langle \varphi \rangle \right)}$

Therefore, the dynamic variable coupling constant in string theory contrasts the quantum field theory where it is constant. As long as supersymmetry is unbroken, such scalar fields can take arbitrary values 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 calculate in string theory.

The dilaton acts like a

In supersymmetry the superpartner of the dilaton or here the dilatino, combines with the axion to form a complex scalar field.^{[citation needed]}

The dilaton in quantum gravity

The dilaton made its first appearance in

This combines gravity, quantization, and even the electromagnetic interaction, promising ingredients of a fundamental physical theory. This outcome revealed a previously unknown and already existing natural link between general relativity and quantum mechanics. There lacks clarity in the generalization of this theory to 3 + 1 dimensions. However, a recent derivation in 3 + 1 dimensions under the right coordinate conditions yields a formulation similar to the earlier 1 + 1, a dilaton field governed by the logarithmic Schrödinger equation^[5] that is seen in condensed matter physics and superfluids. The field equations are amenable to such a generalization, as shown with the inclusion of a one-graviton process,^[6] and yield the correct Newtonian limit in d dimensions, but only with a dilaton. Furthermore, some speculate on the view of the apparent resemblance between the dilaton and the Higgs boson.^[7] However, there needs more experimentation to resolve the relationship between these two particles. Finally, since this theory can combine gravitational, electromagnetic, and quantum effects, their coupling could potentially lead to a means of testing the theory through cosmology and experimentation.

Dilaton action

The dilaton-gravity action is

${\displaystyle \int d^{D}x\,{\sqrt {-g}}\left[{\frac {1}{2\kappa }}\left(\Phi R-\omega \left[\Phi \right]{\frac {g^{\mu \nu }\partial _{\mu }\Phi \partial _{\nu }\Phi }{\Phi }}\right)-V[\Phi ]\right].}$

This is more general than Brans–Dicke in vacuum in that we have a dilaton potential.

See also

• CGHS model
• R = T model
• Quantum gravity

Citations