Causal Dynamical Triangulations| Causal Dynamical Triangulations |
In General
> s.a. Triangulations; Wilson Loops.
* Idea: An approach to quantum
gravity that takes inspiration from lattice field theory and statistical mechanics;
The difference with respect to other dynamical triangulations is that the geometry
is Lorentzian and one considers only triangulations admitting regular foliations.
* Results: Both in 3 and 4 spacetime
dimensions a geometric phase has been identified in which the large scale properties
of the average spacetime are sufficiently classical, and spacetime emerges dynamically
from the sum over histories.
@ Reviews: Ambjørn et al CP(06)ht/05,
in(09)ht/06;
Alpert SA(07)feb; Loll CQG(08)-a0711;
Ambjørn et al SA(08)jul,
LNP(10)-a0906,
in(12)-a1004;
Forcier a1109-MS [introduction];
Ambjørn et al PRP(12)-a1203 [and UV fixed point],
a1302-ch,
a1302-conf;
Cooperman FP(15)-a1410 [concise yet comprehensive introduction];
Ambjørn et al a1509-MG14 [recent results];
Glaser & Loll CR(17)-a1703 [and cosmology];
Loll CQG(20)-a1905.
@ General references: Markopoulou & Smolin NPB(06)ht/04 [varying lapse];
Benedetti PhD(07)-a0707 [analytical];
Zohren PhD(08)-a0905;
Durhuus et al JSP(10)-a0908 [spectral dimension];
Ambjørn et al PLB(10)-a1001 [geometry];
Kommu CQG(12)-a1110 [independent verification of results];
Giasemidis PhD(13)-a1310 [graph toy models and spectral dimcnsion];
Glaser a1409-PhD;
Clemente et al PRD(19)-a1903,
a1912-proc [spectral methods].
@ Renormalization:
Ambjørn et al CQG(14)-a1405
& CQG+ [group flow];
Cooperman GRG(16)-a1406;
Ambjørn et al a1906 [possible UV fixed point].
@ Continuum limit: Benedetti et al PRD(07)-a0704 [and Hamiltonian];
Benedetti & Henson PRD(09)-a0911 [de Sitter space as semiclassical ground state];
Ambjørn et al NPB(11)-a1102,
Trzesniewski MS(10)-a1102 [4D];
Smit JHEP(13)-a1304 [continuum interpretation];
Cooperman a1604.
@ Phase structure: Ambjørn et al PRL(11)-a1108 [evidence for a second-order phase transition];
Ambjørn et al PRD(12)-a1205 [first-order and second-order];
Ambjørn et al JHEP(15)-a1503 [signature change];
Coumbe et al JHEP(16)-a1510;
Ambjørn et al EPJC(17)-a1610;
Clemente & D'Elia PRD(18)-a1804 [eigenvalues of the Laplace-Beltrami operator];
Ambjørn et al CQG(19)-a1904 [critical phenomena].
@ Topology change: Westra PhD-a0810;
Ambjørn & Budd JPA(13) [generalized causal dynamical triangulations];
> s.a. topology change.
@ 2D: Ambjørn & Loll NPB(98)ht [initial idea];
Ansari & Markopoulou NPB(05)ht [as a spin system];
Loll et al AIP(06)ht [sum over topologies];
Zohren MS(05)ht/06 [analytic results, rev];
Benedetti & Loll GRG(07)gq/06 [counting graphs, and matter behavior];
Ambjørn et al JHEP(07)-a0709 [with partial lifting of causality constraint];
Ambjørn et al APPB-a0911-ln [survey];
Atkin PhD(11)-a1111;
Fuji et al PLB(11) [with extended interactions];
Ambjørn PLB(12) [and baby universes];
Ambjørn & Ipsen PLB(13) [universality];
Ambjørn et al MPLA(15)-a1412 [coupled to scalar fields, spectral dimension];
Ambjørn & Watabiki PLB(15)-a1505 [string field theory model];
Ambjørn et al a2003 [zero-temperature criticality];
> s.a. cosmological constant problem.
@ 3D: Ambjørn et al NPB(01)ht [and 4D];
Ambjørn et al NPPS(02)hl;
Dittrich & Loll PRD(02);
Konopka PRD(06)ht/05 [varying lapse];
Sachs a1110 [power spectrum of quantum fluctuations];
Cooperman & Miller CQG(14)-a1305 [transition amplitudes];
Budd & Loll PRD(13)-a1305 [for torus topology];
Bernabei & Thaler a1412 [central limit theorem];
Cooperman et al CQG(17)-a1610 [Lorentzian vs Euclidean de Sitter space];
Cooperman CQG(18)-a1711 [spectral dimension];
Durhuus & Jonsson a1712 [structure of spatial slices].
@ 3D, without a preferred foliation: Jordan & Loll PLB(13)-a1305;
Jordan & Loll PRD(13)-a1307 [emergence of de Sitter space].
@ 4D: Ambjørn et al PRL(04)ht;
Ambjørn et al PRL(05)ht [small-scale spectral dimension],
PRL(08)-a0712,
PRD(08)-a0807,
PLB(10)-a1001 [quantum de Sitter universe];
Durhuus & Jonsson CMP(15)-a1408 [bound on the number of causal triangulations];
Gizbert-Studnicki PhD(14)-a1510 [effective action];
Gizbert-Studnicki APPB-a1704 [phase structure];
Ambjørn et al a2007 [dynamical fractal geometries].
@ 4D, toroidal topology: Ambjørn et al PRD(16)-a1604 [impact of spatial topology];
Ambjørn et al NPB(17)-a1705,
JHEP(18)-a1802;
Gizbert-Studnicki APPB-a1912-conf [phase transitions];
Ambjørn et al a2103 [overview].
@ 4D, transfer-matrix approach:
Görlich PhD(10)-a1111,
a1302-proc;
Ambjørn et al JHEP(14)-a1403.
@ Related topics: Sisko et al a1201 [uniform infinite causal triangulations];
Giasemidis et al JPA(12),
a1209-proc
[random multigraphs, random walk and scale-dependent spectral dimension];
Cooperman PRD(14)-a1410 [scale-dependent homogeneity measures];
> s.a. spacetime dimensionality [reduction].
Models, Phenomenology > s.a. minisuperspace
quantum cosmology; quantum gravity and cosmology.
* Cosmology: CDT predicts that the
(renormalized) cosmological constant is positive, but not a specific value for it.
@ References: Mielczarek EPL(17)-a1503 [dispersion relations and cosmological perturbations],
a1512-MG14.
Variations, Related Theories and Generalized Settings
@ General references: Freedman a1008
[for a formal chain of combinatorial spacetimes without predetermined dimensionality];
Sisko et al JSP(13)-a1203 [growth process for causal triangulations by elementary moves].
@ Relationship with asymptotic safety: Ambjørn et al LNP-a1007 [and entropic gravity];
Coumbe & Jurkiewicz JHEP(15)-a1411 [from dimensional reduction].
@ Relationship with Hořava-Lifshitz gravity:
Ambjørn et al PLB(10)-a1002;
Anderson et al PRD(12)-a1111;
Ambjørn et al PLB(13)-a1302 [2D CDT is 2D Hořava-Lifshitz quantum gravity];
Ambjørn et al IJMPD(13)-a1305;
Benedetti & Henson CQG(15)-a1410
+ CQG+ [spacetime condensation];
> s.a. hořava-lifshitz gravity.
@ And other approaches / models:
Ambjørn et al PLB(08),
Benedetti & Henson PLB(09)-a0812 [and matrix models];
Ambjørn et al JPCS(10)-a1004 [and stochastic quantization];
Kawabe PTEP(16)-a1604 [generalized cdt of tensor model];
> s.a. Dimer Models; Potts Model [coupled to gravity].
@ Variations: Khavkine et al CQG(10)-a1002 [coupled to a pointlike mass];
Atkin & Zohren JHEP(12) [multi-critical CDT, quantum geometry];
Loll & Ruijl PRD(15)-a1507 [locally causal dynamical triangulations];
Vojinović PRD(16)-a1506 [in the spincube model];
Ambjørn et al a2105 with [scalar fields];
> s.a. ising model.
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