Inparticle physics, the hypotheticaldilaton is a particle of ascalar field${\displaystyle \phi }$ that appears in theories withextra dimensions when the volume of the compactified dimensions varies. It appears as aradion inKaluza–Klein theory'scompactifications of extradimensions. InBrans–Dicke theory of gravity,Newton's constant is not presumed to be constant but instead 1/G is replaced by ascalar field${\displaystyle \phi }$ and the associated particle is the dilaton.

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-dimensionaleffective theory.

Although string theory naturally incorporatesKaluza–Klein theory that first introduced the dilaton,perturbative string theories such astype I string theory,type II string theory, andheterotic string theory already contain the dilaton in the maximal number of 10 dimensions. However,M-theory in 11 dimensions does not include the dilaton in its spectrum unlesscompactified. The dilaton intype IIA string theory parallels theradion of M-theory compactified over a circle, and the dilaton in   E₈ × E₈  string theory parallels the radion for theHořava–Witten model. (For more on the M-theory origin of the dilaton, see Berman & Perry (2006).^[1])

Instring theory, there is also a dilaton in theworldsheet CFT –two-dimensional conformal field theory. Theexponential of itsvacuum expectation value determines thecoupling constantg and theEuler characteristic χ = 2 − 2g   as$\frac{1}{2\pi }\int R=\chi$ for compact worldsheets by theGauss–Bonnet theorem, where the genusg counts the number of handles and thus the number of loops or string interactions described by a specific worldsheet.

${\displaystyle g=\exp \left(⟨\phi ⟩\right)}$

Therefore, the dynamic variable coupling constant in string theory contrasts thequantum field theory where it is constant. As long as supersymmetry is unbroken, such scalar fields can take arbitrary valuesmoduli. However,supersymmetry breaking usually creates apotential 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 aBrans–Dicke scalar, with the effectivePlanck scale depending uponboth the string scale and the dilaton field.

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

The dilaton made its first appearance inKaluza–Klein theory, a five-dimensional theory that combinedgravitation andelectromagnetism. It appears instring theory. However, it has become central to the lower-dimensional many-bodied gravity problem^[2] based on the field theoretic approach ofRoman Jackiw. The impetus arose from the fact that complete analytical solutions for the metric of a covariantN-body system have proven elusive in general relativity. To simplify the problem, the number of dimensions was lowered to 1 + 1 – one spatial dimension and one temporal dimension. This model problem, known asR = T theory,^[3] as opposed to the generalG = T theory, was amenable to exact solutions in terms of a generalization of theLambert W function. Also, the field equation governing the dilaton, derived fromdifferential geometry, as theSchrödinger equation could be amenable to quantization.^[4]

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 thelogarithmic Schrödinger equation^[5] that is seen incondensed matter physics andsuperfluids. 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 ind dimensions, but only with a dilaton. Furthermore, some speculate on the view of the apparent resemblance between the dilaton and theHiggs 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.

The dilaton-gravity action is

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

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

• CGHS model
• R = T model
• Quantum gravity
• List of hypothetical particles

• Hypothetical elementary particles
• String theory
• Supersymmetry

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