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 Aa, 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] = \(1\over16\pi G\)∫ dv (R − \(1\over2\)gabaφbφ + \(1\over4\)exp{χφ} Fab Fab) .

@ 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].
@ Related topics: Álvarez & Gómez PLB(00)ht [soft dilaton theorem]; Cavaglià MPLA(00)ht [Weyl invariance].
> Related phenomenology: Screening; tests of newtonian gravity [constraints].
> And quantum gravity: see anomaly; asymptotic safety in quantum gravity.
> Online resources: see Wikipedia page.

Specific Models and Phenomenology > 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].
@ As dark matter: Dick ht/96; Cho & Kim PRD(09)-a0711; Kennedy et al PRL(20) [constraints on interaction with ordinary matter].
@ Other cosmology: Cabo & Amezaga ht/99-conf [as inflaton, and redshift]; 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; cosmological constant; dark energy; dark matter.
@ 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 = dBAF (which implies dH = −FF),

SADJ = M dv [exp{−2Φ}(R + 4 ∇aΦ ∇aΦ − \(1\over3\)Habc HabcFab Fab) + \(\cal L\)matter]
SADE = M dv [R − 2 ∇aΦ ∇a Φ − \(1\over3\)exp{−4Φ} Habc Habc − exp{−2Φ} Fab Fab + exp{4Φ} \(\cal L\)matter(exp{2Φ}g)] .

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