scholarly journals Fixed point structure of the conformal factor field in quantum gravity

2016 ◽  
Vol 94 (12) ◽  
Author(s):  
Juergen A. Dietz ◽  
Tim R. Morris ◽  
Zoë H. Slade
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
Conformal Factor

scholarly journals Quantum gravity, renormalizability and diffeomorphism invariance

2018 ◽  
Vol 5 (4) ◽  
Author(s):  
Tim Morris
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Renormalization Group ◽  
Quantum Gravity ◽  
Master Equation ◽  
Conformal Factor ◽  
Quantum Master Equation ◽  
First Order ◽  
Diffeomorphism Invariance ◽  
Brst Cohomology

We show that the Wilsonian renormalization group (RG) provides a natural regularisation of the Quantum Master Equation such that to first order the BRST algebra closes on local functionals spanned by the eigenoperators with constant couplings. We then apply this to quantum gravity. Around the Gaussian fixed point, RG properties of the conformal factor of the metric allow the construction of a Hilbert space \Ll of renormalizable interactions, non-perturbative in \hbarℏ, and involving arbitrarily high powers of the gravitational fluctuations. We show that diffeomorphism invariance is violated for interactions that lie inside \Ll, in the sense that only a trivial quantum BRST cohomology exists for interactions at first order in the couplings. However by taking a limit to the boundary of \Ll, the couplings can be constrained to recover Newton’s constant, and standard realisations of diffeomorphism invariance, whilst retaining renormalizability. The limits are sufficiently flexible to allow this also at higher orders. This leaves open a number of questions that should find their answer at second order. We develop much of the framework that will allow these calculations to be performed.

scholarly journals CONFORMAL DYNAMICS OF QUANTUM GRAVITY WITH TORSION

1993 ◽  
Vol 08 (11) ◽  
pp. 979-985 ◽  
Author(s):  
I. ANTONIADIS ◽  
S. D. ODINTSOV
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
Conformal Factor ◽  
Coupling Constants ◽  
Stable Fixed Point ◽  
Scalar Theory ◽  
Trace Anomaly ◽  
Matter Interaction ◽  
Conformal Dynamics

The trace anomaly induced dynamics of the conformal factor is investigated in four-dimensional quantum gravity with torsion. The constraints for the coupling constants of torsion matter interaction are obtained in the ir stable fixed point of the effective scalar theory.

scholarly journals Dimension and Dimensional Reduction in Quantum Gravity

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 83 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
Dimensional Reduction ◽  
Short Distance ◽  
Evidence Based ◽  
Two Dimensional ◽  
Anomalous Scaling ◽  
Lines Of Evidence ◽  
Quantum Spacetime

If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short-distance dimensional reduction. I will review the evidence for this behavior, emphasizing the physical question of what one means by “dimension” in a quantum spacetime, and will discuss possible mechanisms that could explain the universality of this phenomenon.

scholarly journals WILSONIAN BLACK HOLE ENTROPY IN QUANTUM GRAVITY

1996 ◽  
Vol 11 (16) ◽  
pp. 2823-2834
Author(s):  
SERGEI D. ODINTSOV ◽  
YONGSUNG YOON
Keyword(s):  
Black Hole ◽  
Renormalization Group ◽  
Quantum Gravity ◽  
Black Hole Entropy ◽  
Conformal Factor ◽  
Infrared Region ◽  
Coupling Constants ◽  
Effective Theory ◽  
Free Form ◽  
Renormalization Group Equations

Using the Wilsonian procedure (renormalization group improvement) we discuss the finite quantum corrections to black hole entropy in renormalizable theories. In this way, the Wilsonian black hole entropy is found for GUT’s (of asymptotically free form, in particular) and for the effective theory for the conformal factor aiming to describe quantum gravity in the infrared region. The off-critical regime (where the coupling constants are running) for the effective theory for the conformal factor in quantum gravity (with or without torsion) is explicitly constructed. The corresponding renormalization group equations for the effective couplings are found using the Schwinger-DeWitt technique for the calculation of the divergences of the fourth order operator.

YUKAWA MODEL IN CURVED SPACETIME

1995 ◽  
Vol 10 (15n16) ◽  
pp. 1091-1100
Author(s):  
E. ELIZALDE ◽  
S.D. ODINTSOV
Keyword(s):  
Fixed Point ◽  
Conformal Factor ◽  
Bound State ◽  
Usual Sense ◽  
Stable Fixed Point ◽  
Coupling Constant ◽  
Yukawa Model ◽  
Curved Spacetime ◽  
Cosmological Constant Problem ◽  
Njl Model

The Yukawa model in curved spacetime (renormalizable in the usual sense) is considered near the critical point, using the 1/N-expansion and renormalization group techniques. The equivalence of this model with the standard NJL model is proven. The behavior of the graviton-scalar bound state coupling constant near the ir stable fixed point ξ=1/6 is discussed. The effective potential is calculated and a dynamically generated fermionic mass is found. Some applications to quantum gravity which make explicit use of the 1/N-expansion are briefly discussed. In particular, a possible solution of the cosmological constant problem within the framework of conformal factor dynamics is pointed out.

THE CONFORMAL FACTOR AND THE COSMOLOGICAL CONSTANT

1990 ◽  
Vol 05 (19) ◽  
pp. 3811-3829 ◽  
Author(s):  
STEVEN B. GIDDINGS
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Path Integral ◽  
Conformal Factor ◽  
Positive Cosmological Constant ◽  
Lorentzian Signature ◽  
Wrong Sign ◽  
Euclidean Signature

The issue of the conformal factor in quantum gravity is examined for Lorentzian signature spacetimes. In Euclidean signature, the “wrong” sign of the conformal action makes the path integral undefined, but in Lorentzian signature this sign is tied to the instability of gravity and once this is accounted for the path integral should be well-defined. In this approach it is not obvious that the Baum-Hawking-Coleman mechanism for suppression of the cosmological constant functions. It is conceivable that since the multiuniverse system exhibits an instability for positive cosmological constant, the dynamics should force the system to zero cosmological constant.

scholarly journals CONFORMAL FACTOR DYNAMICS IN THE 1/N EXPANSION

1995 ◽  
Vol 10 (09) ◽  
pp. 733-739 ◽  
Author(s):  
E. ELIZALDE ◽  
S. D. ODINTSOV
Keyword(s):  
Renormalization Group ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Effective Potential ◽  
Bound States ◽  
Conformal Factor ◽  
Effective Theory ◽  
Cosmological Constant Problem ◽  
New Model

We suggest to consider conformal factor dynamics as applying to composite bound states, in the framework of the 1/N expansion. In this way, a new model of effective theory for quantum gravity is obtained. The renormalization group (RG) analysis of this model provides a framework to solve the cosmological constant problem, since the value of this constant turns out to be suppressed, as a result of the RG contributions. The effective potential for the conformal factor is also found.

scholarly journals Ultraviolet stable fixed point and scaling relations in (2 + ϵ)-dimensional quantum gravity

1993 ◽  
Vol 404 (3) ◽  
pp. 684-714 ◽  
Author(s):  
Hikaru Kawai ◽  
Yoshihisa Kitazawa ◽  
Masao Ninomiya
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
Scaling Relations ◽  
Stable Fixed Point

scholarly journals ONE-LOOP DIVERGENCES OF QUANTUM GRAVITY USING CONFORMAL PARAMETRIZATION

2000 ◽  
Vol 15 (38n39) ◽  
pp. 2335-2343 ◽  
Author(s):  
GUILHERME DE BERREDO-PEIXOTO ◽  
ANDRÉ PENNA-FIRME ◽  
ILYA L. SHAPIRO
Keyword(s):  
Quantum Gravity ◽  
Conformal Invariance ◽  
Conformal Factor ◽  
Conformal Metric ◽  
Gauge Fixing ◽  
Conformal Gauge ◽  
Independent Variable ◽  
The One ◽  
Conformal Parametrization ◽  
Scalar Gravity

We calculate the one-loop divergences for quantum gravity with cosmological constant, using new parametrization of quantum metric. The conformal factor of the metric is treated as an independent variable. As a result the theory possesses an additional degeneracy and one needs an extra conformal gauge fixing. We verify the on-shell independence of the divergences from the parameter of the conformal gauge fixing, and find a special conformal gauge in which the divergences coincide with the ones obtained by 't Hooft and Veltman (1974). Using conformal invariance of the counterterms, one can restore the divergences for the conformal metric–scalar gravity.

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