Asymptotic Safety in Quantum Gravity  

In General > s.a. non-renormalizable theories; renormalization of quantum gravity.
* Idea: Quantum gravity with a cosmological constant has a non-Gaussian UV fixed point; The first-order, tetrad + connection form also has one, probably inequivalent to the metric gravity one.
* Underlying physical mechanism: (Nink & Reuter 2012) The inverse propagator for metric fluctuations contains two pieces, a covariant Laplacian and a curvature-dependent potential term; These can be interpreted, respectively, as diamagnetic and paramagnetic-type interactions of the metric fluctuations of spacetime, considered as a polarizable medium, with the background gravitational field.
@ Reviews: Niedermaier CQG(07)gq/06; Niedermaier & Reuter LRR(06); Percacci in(09)-a0709 [rev]; Litim PoS-a0810; Percacci a1110-proc [short introduction]; Reuter & Saueressig NJP(12)-a1202 [pedagogical introduction]; Reuter & Saueressig LNP(12)-a1205 [and possible multifractal structure]; Ambjørn et al NJP(12) [focus issue]; Eichhorn a1709-proc.
@ General references: Weinberg in(79); Souma PTP(99)ht, gq/00; Lauscher & Reuter PRD(02)ht/01, CQG(02)ht/01, IJMPA(02)ht/01; Litim PRL(04)ht/03 [Euclidean, arbitrary dimension]; Percacci & Perini CQG(04)ht [fixed point]; Percacci PRD(06)ht/05; Emoto gq/06-conf; Ward MPLA(08)-a0808 [predictions for G and Λ, resummation techniques]; Codello et al AP(09) [Wilsonian renormalization group equation]; Niedermaier PRL(09), NPB(10) [from perturbation theory]; Daum & Reuter PLB(12)-a1012 [using the Holst action]; Manrique et al PRL(11)-a1102 [Lorentzian]; Benedetti NJP(12)-a1107 [on shell]; Litim & Satz a1205 [limit cycles]; Nink & Reuter JHEP(13)-a1208, IJMPD(13)-a1212-MG13 [underlying physical mechanism]; Christiansen et al a1209 [renormalization group and fixed points]; Benedetti EPL(13)-a1301 [number of relevant operators]; Falls et al JHEP(16)-a1410 [strong support for the conjecture]; Falls a1503 [scaling behaviour]; Biemans et al PRD(17)-a1609; Gionti a1805-proc [Hamiltonian formalism].
@ Related topics: Reuter & Weyer PRD(09)-a0804 [and diffeomorphism invariance]; Reuter & Weyer GRG(09)-a0903-conf [role of background independence]; Benedetti et al AIP(09)-a0909 [role of higher-derivative terms]; Manrique et al AP(11)-a1005 [bimetric renormalization-group flow]; Falls JHEP(16)-a1408 [and the cosmological constant]; Nink a1701-PhD [background independence and unitarity, and the 2D case]; Houthoff et al EPJC(17)-a1705 [ADM formulation on a background spacetime with topology S1 × Sd]; Einhorn & Jones PRD(17)-a1710 [asymptotic freedom]; > s.a. UV Completion.

Matter and Other Gravity Theories > s.a. approaches to quantum gravity; deformed special relativity; dynamical triangulations; fractal spacetime.
* With matter: The existence of non-Gaussian renormalization group fixed points is rather generic; In particular, the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety, and there are non-Gaussian fixed points for any number of scalar matter fields.
@ With other variables: Daum & Reuter a1111-proc, AP(13) [vielbein and spin-connection variables, running Immirzi parameter]; Harst & Reuter JHEP(12)-a1203 [tetrad-only gravity]; Harst & Reuter PLB(15)-a1509 [with selfdual/anti-selfdual spin-connection, likely asymptotically safe].
@ With matter: Percacci & Perini PRD(03)ht [scalar field]; Vacca & Zanusso PRL(10)-a1009 [scalar and fermion fields]; Henz et al PLB(13)-a1304 [scalar dilaton]; Donà et al PRD(14) [compatibility of minimally-coupled matter]; Meibohm et al PRD(16)-a1510 [scalar and fermion fields]; Donà et al PRD(16)-a1512 [scalar]; Meibohm & Pawlowski EPJC(16)-a1601 [chiral fermions]; Biemans et al JHEP(17)-a1702 [gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields, ADM formalism]; Christiansen et al PRD(18)-a1710; Eichhorn et al a1804 [gravity + scalar, universality].
@ Higher-order gravity: Codello & Percacci PRL(06)ht, Codello et al IJMPA(07)-a0705 [f(R) gravity]; Benedetti et al MPLA(09)-a0901; Ohta CQG(12)-a1205 [higher-derivative gravity]; Ohta & Percacci CQG(14)-a1308 [in various dimensions]; González-Martín et al PRD(17)-a1704 [asymptotic solutions]; Einhorn & Jones PRD(17)-a1710 [quadratic, without ghosts or tachyons]; Falls et al PRD-a1801; Alkofer & Saueressig a1802 [f(R) gravity coupled to matter].
@ Other gravity theories: Fischer & Litim PLB(06)ht, Litim AIP(06)ht [D > 4]; Reuter & Weyer PRD(09)-a0801 [conformally reduced gravity]; Cai & Easson PRD(12) [effective scalar-tensor theory]; > s.a. hořava gravity [candidate UV completion].

Phenomenology > s.a. black-hole quasinormal modes; dark energy; quantum-gravity effects on geometry [collapse] and particle properties.
@ General references: Hewett & Rizzo JHEP(07)-a0707, Litim & Plehn PRL(08)-a0707 [collider signals]; Litim PTRS(11)-a1102 [applications];
Bonanno PRD(12)-a1203 [effective action, early-universe implications]; Döbrich & Eichhorn JHEP(12)-a1203, Eichhorn a1210-MG13 [photon-photon scattering]; Eichhorn PRD(12) [scalar field self-interactions]; Eichhorn et al a1710 [viability test].
@ Spacetime geometry: Reuter & Schwindt JPA(07)ht/06, JHEP(07) [scale-dependent metric and minimum length]; Manrique & Reuter AP(10)-a0907 [background metric]; Percacci & Vacca CQG(10)-a1008 [emergence and minimal length]; > s.a. singularities in quantum gravity [avoidance].
@ Astrophysics and black holes: Bonanno PoS-a0911 [astrophysical implications]; Becker & Reuter JHEP(12)-a1205, a1212-MG13 [non-trivial boundaries, and black-hole thermodynamics]; Koch et al a1311-conf [black holes]; Koch & Saueressig CQG(14) [structural aspects], IJMPA(14)-a1401 [rev].
@ Cosmology: Fang & Huang EPJC(13)-a1210 [trouble with asymptotically-safe inflation]; Bonanno & Saueressig CRP(17)-a1702 [rev]; > s.a. dark energy.
> Related topics: see fine-structure constant.

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