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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