Dilaton
Field / Gravity |

**In General** > s.a. 2D gravity; 2D
quantum gravity; solutions in general relativity.

* __Idea__: A theory arising
in dimensional reduction from higher-dimensions (Kaluza-Klein theory, large
extra dimensions, string theory), which includes a U(1) gauge field *A*_{a},
and depends on a constant *χ*; The dilaton also arises as the Goldstone
boson of spontaneously broken conformal field theories (in flat spacetime).

* __Action__: If *F*_{ab} is the curvature of *A*_{a},

*S*[*g*,* A*, *φ*]
= \(1\over16\pi G\)∫ d*v* (*R* – \(1\over2\)*g*^{ab}∂_{a}*φ* ∂_{b}*φ*
+ \(1\over4\)exp{*χ**φ*} *F*_{ab}* F*^{ab})
.

@ __General references__: Nojiri & Odintsov IJMPA(01)
[quantum, *D* = 2, 4, 5]; Sundrum
ht/03 [as
scalar analog of general relativity].

@ __Dynamics__: Burton & Mann CQG(98)
[Palatini, *N*-dimensional]; Cadoni & Mana
CQG(01)gq/00 [Hamiltonian with boundary].

@ __Inflaton__: Cabo & Amezaga ht/99-conf [and redshift].

@ __Related topics__: Álvarez & Gómez
PLB(00)ht [soft dilaton theorem];
Cavaglià MPLA(00)ht [Weyl invariance].

> __Related phenomenology__: see cosmological
constant; dark energy;
dark matter; Screening;
tests of newtonian gravity [constraints].

> __And quantum gravity__: see anomaly; asymptotic safety in quantum gravity.

**Specific Models and Solutions** > s.a. black-hole
solutions; gauge-theory solutions; solutions
of general relativity.

@ __With other matter__: Meyer ht/05-proc
[fermions]; Grumiller & Meyer CQG(06)ht [Dirac
fermion, quantum].

@ __Black holes__: Gibbons & Maeda NPB(88);
Garfinkle et al PRD(91);
Chan et al NPB(95);
Gibbons & Kallosh PRD(95)ht/94; Kiem & Park; Casadio et al PRD(97);
Casadio & Harms MPLA(99)
[different frames]; Vorontsova & Sharov TMP(05)
[*d*-dimensional Schwarzschild-like].

@ __Cosmology__: Billyard
et al JMP(00)gq;
Chen et al PRD(00)ht [Bianchi I];
Cabo & Brandenberger JCAP(09)-a0806 [stabilized
by fermion masses]; > s.a. bianchi
models.

@ __Quantum cosmology__: Catren & Simeone mp/05-ch;
Ahmed NCB(06)gq [+
pfluid].

@ __Related topics__: Maeda et al PRL(98)gq [naked singularities].

> __Related topics__: see fine-structure constant [spatial variation]; topological defects.

**Axion-Dilaton Gravity** > s.a. axion;
black-hole solutions.

* __Idea__: A theory arising
in the low-energy limit of heterotic string theory, via toroidal compactification to 4D.

* __Action__: If *H* =
d*B* – *A* *∧ F* (which implies d*H* =
–*F* ∧ *F*),

*S*^{AD}_{J} =
∫_{M} d*v* [exp{–2Φ}(*R* +
4 ∇_{a}Φ ∇^{a}Φ –
\(1\over3\)*H*_{abc}* H*^{abc} –
*F*_{ab}* F*^{ab})
+ \(\cal L\)_{matter}]

*S*^{AD}_{E} =
∫_{M} d*v* [*R* –
2 ∇_{a}Φ ∇^{a }Φ – \(1\over3\)exp{–4Φ} *H*_{abc}* H*^{abc}
– exp{–2Φ} *F*_{ab}* F*^{ab} +
exp{4Φ} \(\cal L\)_{matter}(exp{2Φ}*g*)]
.

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jan 2016