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 a1707 [exact RG flow]; Doboszewski & Linnemann a1712 [how to formulate].

@ __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).

@

@

>

**Perturbative Non-Renormalizability** > s.a. renormalization / gravitation; quantum
gravity.

* __The issue__: The theory
appears non-renormalizable (around *g*_{ab} = *η*_{ab})
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.

@ __References__: Deser RMP(57);
Deser & van Nieuwenhuizen PRD(74)
[Einstein-Maxwell theory], PRD(74)
[Einstein-Dirac theory], et al PRD(74)
[Einstein-Yang-Mills theory]; '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]; > s.a. minisuperspace [and
wormholes].

**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 mass of a charged particle in general relativity should
satisfy

*mc*^{2} = *m*_{0}*c*^{2} +
*e*^{2}/*ε* –
*Gm*^{2}/*ε* ,

i.e., *m* = 2*e* *G*^{–1/2} for *ε* → 0,
independent of *m*_{0} (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 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]; > 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].

@ __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].

@ __And phenomenology__: Rodrigues et al JCAP(10), PoS-a1301 [corrections to
galaxy
rotation
curves].

@ __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].

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