Renormalization of Quantum Gravity  

In General > s.a. renormalization group [including holographic renormalization].
@ General references: Christiansen et al PRD(16)-a1403 [global phase diagram]; Falls a1702 [and asymptotic safety]; de Alwis JHEP(18)-a1707 [exact RG flow]; Doboszewski & Linnemann FP(18)-a1712 [how to formulate]; Dhumuntarao a1807 [renormalization group flow and stress-energy tensor as source for heat equation]; Wiesendanger a1905 [renormalizability]; Gustavsson a1911 [with boundaries and corners]; Falls a2004 [manifestly background-independent approach].
@ Ultraviolet behavior: Christiansen et al PRD(15)-a1506 [functional renormalisation group approach]; > s.a. asymptotic safety.
@ Effective G and cosmological constant: Parker gq/98/PRL [and cosmology]; Reuter & Weyer PRD(04)gq/03 [improved action]; Shapiro et al JCAP(05).
@ Related topics: Smolin NPB(79) [and asymptotically scale-invariant geometry]; Jacobson & Satz PRD(14)-a1308 [renormalization of the Gibbons-Hawking boundary term]; Slovick MPLA(18)-a1309 [and symmetry of the functional measure]; Gies et al PRD(15)-a1507 [parametrization dependence of the renormalization group flow]; Solodukhin PLB(16)-a1509, Coumbe IJMPD(19)-a1804 [and metric redefinition]; Morris SciPost(18)-a1806 [and diffeomorphism invariance]; Ambjørn et al a2002 [without a fixed background geometry]; Martini et al a2105 [universality class].
@ Diffeomorphism-invariant Wilsonian (exact) renormalization group: Morris & Preston JHEP(16)-a1602; Preston a1612-PhD.
> Related topics: see Confinement; effective theories; Immirzi Parameter; newton's gravitational constant [running]; spin networks.

Perturbative Renormalization > s.a. renormalization / gravitation; quantum gravity.
* The non-renormalizability issue: The theory appears non-renormalizable (around gab = ηab) from power counting; This would not imply non-existence of quantum gravity, but by itself if quantum gravity was an ordinary theory it would be close to a kiss of death.
* Argument for non-renormalizability: The coupling constant G has dimensions of squared length.
* Proposed approaches: Study methods for handling non-renormalizable theories; Choose appropriate matter terms (> see supergravity); Euclideanize, study instantons and sum over manifolds; Include higher-derivative terms.
@ General references: Deser RMP(57); 't Hooft & Veltman AIHP(74); Deser in(75); Deser et al in(75); ·Weinberg in(79); Martellini PRL(83) [with cosmological constant]; Goroff & Sagnotti NPB(86) [non-renormalizable ultraviolet divergences]; Crane & Smolin NPB(86) [virtual black holes and fermions]; Deser et al PLB(89); van de Ven NPB(92) [non-renormalizable infinity in the two-loop effective action]; Shomer a0709 [pedagogical]; Marin a1002 [reformulation of the theory]; Morris JHEP(18)-a1802 [conformal sector]; Morris a1805-GRF, Das et al IJMPD(18)-a1805-GRF [perturbatively renormalizable theory]; Lavrov & Shapiro PRD(19)-a1902 [gauge-invariant]; Kellett et al a2006 [continuum limit]; > s.a. minisuperspace [and wormholes].
@ With matter: Deser & van Nieuwenhuizen PRD(74) [Einstein-Maxwell theory], PRD(74) [Einstein-Dirac theory], et al PRD(74) [Einstein-Yang-Mills theory].

Non-Perturbative Renormalization > s.a. 3D quantum gravity; approaches to quantum gravity; canonical and covariant quantum gravity.
* Idea: The usual non-renormalizability arguments are not reliable for a theory without a background metric; One needs to use different ones, and some arguments, both classical and quantum, point to the possibility that the theory, despite being non-renormalizable with the usual perturbative methods, is non-perturbatively renormalizable (although Witten claimed it is not, because the 4D action is cubic),
- Classical analog: The total

mc2 = m0c2 + e2/εGm2/ε ,

i.e., m = 2e G−1/2 for ε → 0, independent of m0 (nice for particles from geometry); This comes from the diffeomorphism invariance of the theory and the fact that therefore energy is expressed as a surface integral at infinity.
- Examples from other theories: The 3D Gross-Neveu model; Gravity is exactly soluble in 3D, where can be written as a theory with quadratic action, where one perturbs around the zero triad [@ Witten NPB(88)].
@ General references: Arnowitt et al PRL(60); in Ashtekar; Weinberg in(79); Smolin NPB(82); Crane & Smolin NPB(86); Kawai & Ninomiya NPB(90); Abe & Nakanishi MPLA(95); Maeda & Sakamoto PRD(96)ht [strong-coupling expansion]; Hamada PTP(02)ht [higher-order renormalization]; Kreimer AP(08)-a0705, in(09)-a0805 [from structure of Dyson-Schwinger equations]; Percacci PoS-a0910; Hamber a1002-MG12; Knorr CQG(18)-a1710 [new approximation scheme].

Other Theories of Gravity > s.a. 2D quantum gravity; higher-order gravity; modified theories [hořava gravity].
@ General references: Haba ht/02 [Brans-Dicke theory]; Nikolić a0708 [in linearized gravity]; Freidel et al PRD(09)-a0905 [3D Boulatov model, group-field-theory approach]; Narain & Percacci CQG(10)-a0911, Narain & Rahmede CQG(10)-a0911 [scalar-tensor theories]; Pagani & Percacci CQG(15)-a1506 [with torsion and non-metricity]; Finocchiaro & Oriti a2004 [group field theory]; Bajardi et al Univ-a2105; > s.a. Topologically Massive Gravity.
@ Gravity and coupled matter: Granda EPL(98)ht/05 [general relativity + N scalars, G and Λ], NCB(99)ht/05 [general relativity + N-spinor]; Ibiapina Bevilaqua et al CQG(16)-a1506 [Einstein gravity coupled to scalar electrodynamics, effective field theory]; Ghodsi & Siahvoshan a2105 [with a scalar feld, d+1 dimensions].
@ Discrete models: Requardt gq/02; Oeckl NPB(03)gq/02 [without background]; > s.a. dynamical triangulations; lattice gravity; regge calculus; spin-foam models.
@ Functional renormalization group: Benedetti & Caravelli JHEP(12)-a1204 [and local potential approximation]; Donà & Percacci PRD(13)-a1209 [with fermions and tetrads]; Nagy et al PRD(13)-a1307 [critical exponents]; Reuter & Schollmeyer AP(16)-a1509 [on a theory space]; Alkofer a1809-MS [with one extra compact dimension]; Reuter & Saueressig 19; Barra et al a1910 [and gauge dependence].
@ Related topics: Reuter & Saueressig PRD(02)ht/01, PRD(02)ht [non-local truncation of general relativity]; Dienes & Mafi PRL(02) [compactification geometry]; Bonanno & Reuter JHEP(05)ht/04 [comparison between renormalization group equations]; Anselmi JHEP(07)ht/06 [semiclassical]; Canfora PRD(06)ht [UV behavior at large N]; Neugebohrn PhD(07)-a0704 [and effective actions]; Narain & Percacci APPB-a0910-proc [beta function, scheme dependence]; Donkin & Pawlowski a1203 [phase diagram of quantum gravity from diffeomorphism-invariant RG-flows].
> Related topics: see cosmological constant [running]; general-relativistic cosmology [with varying G and Λ]; quantum gravity phenomenology.

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