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{{technical|date=October 2013}}
In [[particle physics]], a '''dilaton''' is a [[hypothetical particle]].  It also appears in [[Kaluza-Klein theory]]'s [[compactification (physics)|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]].
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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 [[Compactification (physics)|compactified]]. In fact, the dilaton in [[type IIA string theory]] is actually the [[radion (physics)|radion]] of M-theory compactified over a circle, while the dilaton in {{nowrap|E<sub>8</sub> × E<sub>8</sub>}} string theory is the radion for the [[Hořava&ndash;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{{Clarify|date=September 2013}}. The [[exponential function|exponential]] of its [[vacuum expectation value]] determines the [[coupling constant]] ''g'', as {{nowrap|∫R {{=}} 2πχ}} for compact worldsheets by the [[Gauss-Bonnet theorem]] and the [[Euler characteristic]]  {{nowrap|χ {{=}} 2 − 2''g''}}, 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.
 
:<math>g = \exp(\langle \phi \rangle)</math>
 
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 space|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 theory|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.
 
== Dilaton action ==
 
The dilaton-gravity action is
:<math>\int d^Dx \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]</math>.
This is more general than Brans–Dicke in that we have a dilaton potential.
 
== See also ==
 
* [[CGHS model]]
* [[R=T model]]
* [[Quantum_gravity#The_dilaton|Quantum Gravity]]
 
==References==
*{{Cite journal |first=Y. |last=Fujii |title=Mass of the dilaton and the cosmological constant |journal=[[Progress of Theoretical Physics|Prog. Theor. Phys.]] |volume=110 |issue=3 |year=2003 |pages=433–439 |doi=10.1143/PTP.110.433 |arxiv = gr-qc/0212030 |bibcode = 2003PThPh.110..433F }}
*{{Cite journal |first=M. |last=Hayashi |first2=T. |last2=Watanabe |first3=I. |last3=Aizawa |lastauthoramp=yes |first4=K. |last4=Aketo |title=Dilatonic Inflation and SUSY Breaking in String-inspired Supergravity |journal=[[Modern Physics Letters]] A |volume=18 |issue=39 |year=2003 |pages=2785–2793 |doi=10.1142/S0217732303012465 |arxiv = hep-ph/0303029 |bibcode = 2003MPLA...18.2785H }}
*{{Cite journal |first=F. |last=Alvarenge |first2=A. |last2=Batista |lastauthoramp=yes |first3=J. |last3=Fabris |title=Does Quantum Cosmology Predict a Constant Dilatonic Field |journal=[[International Journal of Modern Physics]] D |volume=14 |issue=2 |year=2005 |pages=291–307 |doi=10.1142/S0218271805005955 |arxiv = gr-qc/0404034 |bibcode = 2005IJMPD..14..291A }}
*{{Cite arxiv|first=H. |last=Lu |first2=Z. |last2=Huang |first3=W. |last3=Fang |lastauthoramp=yes |first4=K. |last4=Zhang |title=Dark Energy and Dilaton Cosmology |class=hep-th |eprint=hep-th/0409309 |year=2004}}
*{{Cite book |first=Paul S. |last=Wesson |title=Space-Time-Matter, Modern Kaluza-Klein Theory |year=1999 |publisher=World Scientific |location=Singapore |isbn=981-02-3588-7 |page=31 }}
 
{{particles}}
 
[[Category:String theory]]
[[Category:Supersymmetry]]
[[Category:Hypothetical elementary particles]]

Revision as of 18:43, 18 February 2014


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