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/ε − Gm2/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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