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| {{technical|date=October 2013}}
| | The title of the writer is Numbers. His wife doesn't like it the way he does but what he really likes doing is to do aerobics and he's been doing it for fairly a whilst. He used to be unemployed but now he is a meter reader. Minnesota has usually been his house but his spouse desires them to move.<br><br>Feel free to visit my site diet meal delivery ([http://Teeurl.com/healthymealsdelivered68340 click the following article]) |
| 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.
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| 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.
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| 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–Witten model]]. (For more on the M-theory origin of the dilaton, see [http://arxiv.org/abs/hep-th/0601141].)
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| 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.
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| :<math>g = \exp(\langle \phi \rangle)</math>
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| 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.
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| 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.
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| In supersymmetry, the [[superpartner]] of the dilaton is called the '''dilatino''', and the dilaton combines with the [[axion]] to form a complex scalar field.
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| == Dilaton action ==
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| The dilaton-gravity action is
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| :<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>.
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| This is more general than Brans–Dicke in that we have a dilaton potential.
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| == See also ==
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| * [[CGHS model]]
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| * [[R=T model]]
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| * [[Quantum_gravity#The_dilaton|Quantum Gravity]]
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| ==References==
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| *{{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 }}
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| *{{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 }}
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| *{{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 }}
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| *{{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}}
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| *{{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 }}
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| {{particles}}
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| [[Category:String theory]]
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| [[Category:Supersymmetry]]
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| [[Category:Hypothetical elementary particles]]
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