Asymptotic Freedom in the Conformal Quantum Gravity with Matter

1989 ◽  
Vol 37 (3) ◽  
pp. 207-223 ◽  
Author(s):  
I. L. Buchbinder ◽  
O. K. Kalashnikov ◽  
I. L. Shapiro ◽  
V. B. Vologodsky ◽  
J. J. Wolfengaut
Keyword(s):  
Quantum Gravity ◽  
Asymptotic Freedom

Asymptotic freedom and Regge-einstein quantum gravity

1993 ◽  
Vol 30 ◽  
pp. 768-770 ◽  
Author(s):  
Bernd A. Berg ◽  
Balasubramanian Krishnan
Keyword(s):  
Quantum Gravity ◽  
Asymptotic Freedom

scholarly journals Asymptotic freedom and euclidean quantum gravity

1993 ◽  
Vol 404 (1-2) ◽  
pp. 359-382 ◽  
Author(s):  
Bernd A. Berg ◽  
Balasubramanian Krishnan ◽  
Mohammad Katoot
Keyword(s):  
Quantum Gravity ◽  
Asymptotic Freedom

Asymptotic freedom in gauge theories and quantum gravity

1990 ◽  
Vol 33 (1) ◽  
pp. 30-34
Author(s):  
Yu. Yu. Vol'fengaut ◽  
I. L. Shapiro ◽  
E. G. Yagunov
Keyword(s):  
Quantum Gravity ◽  
Gauge Theories ◽  
Asymptotic Freedom

Asymptotic freedom in higher-derivative quantum gravity

1985 ◽  
Vol 159 (4-6) ◽  
pp. 269-274 ◽  
Author(s):  
I.G. Avramidy ◽  
A.O. Barvinsky
Keyword(s):  
Quantum Gravity ◽  
Asymptotic Freedom ◽  
Higher Derivative

scholarly journals Some Remarks on High Derivative Quantum Gravity

1997 ◽  
Vol 12 (32) ◽  
pp. 5711-5734 ◽  
Author(s):  
M. Asorey ◽  
J. L. López ◽  
I. L. Shapiro
Keyword(s):  
Quantum Gravity ◽  
High Derivative ◽  
Einstein Gravity ◽  
Low Energy ◽  
Local Action ◽  
Quantum Corrections ◽  
Asymptotic Freedom ◽  
Low Energies ◽  
Gauge Fixing ◽  
High Derivative Gravity

We analyze the perturbative implications of the most general high derivative approach to quantum gravity based on a diffeomorphism-invariant local action. In particular, we consider the superrenormalizable case with a large number of metric derivatives in the action. The structure of ultraviolet divergences is analyzed in some detail. We show that they are independent of the gauge-fixing condition and the choice of field reparametrization. The cosmological counterterm is shown to vanish under certain parameter conditions. We elaborate on the unitarity problem of high derivative approaches and the distribution of masses of unphysical ghosts. We also discuss the properties of the low energy regime and explore the possibility of having a multiscale gravity with different scaling regimes compatible with Einstein gravity at low energies. Finally, we show that the ultraviolet scaling of matter theories is not affected by the quantum corrections of high derivative gravity. As a consequence, asymptotic freedom is stable under those quantum gravity corrections.

scholarly journals Yang–Mills mass gap at large-N, noncommutative YM theory, topological quantum field theory and hyperfiniteness

2015 ◽  
Vol 24 (06) ◽  
pp. 1530017 ◽  
Author(s):  
Marco Bochicchio
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Quantum Gravity ◽  
Gauge Theories ◽  
Floer Homology ◽  
Asymptotic Freedom ◽  
General Interest ◽  
Yang Mills ◽  
Mass Gap ◽  
Large N

We review a number of old and new concepts in quantum gauge theories, some of which are well-established but not widely appreciated, some are most recent, that may have analogs in gauge formulations of quantum gravity, loop quantum gravity, and their topological versions, and may be of general interest. Such concepts involve noncommutative gauge theories and their relation to the large-N limit, loop equations and the change to the anti-selfdual (ASD) variables also known as Nicolai map, topological field theory (TFT) and its relation to localization and Morse–Smale–Floer homology, with an emphasis both on the mathematical aspects and the physical meaning. These concepts, assembled in a new way, enter a line of attack to the problem of the mass gap in large-NSU(N) Yang–Mills (YM), that is reviewed as well. Algebraic considerations furnish a measure of the mathematical complexity of a complete solution of large-NSU(N) YM: In the large-N limit of pure SU(N) YM the ambient algebra of Wilson loops is known to be a type II1 nonhyperfinite factor. Nevertheless, for the mass gap problem at the leading 1/N order, only the subalgebra of local gauge-invariant single-trace operators matters. The connected two-point correlators in this subalgebra must be an infinite sum of propagators of free massive fields, since the interaction is subleading in [Formula: see text], a vast simplification. It is an open problem, determined by the growth of the degeneracy of the spectrum, whether the aforementioned local subalgebra is in fact hyperfinite. Moreover, the sum of free propagators that occurs in the two-point correlators in the aforementioned local subalgebra must be asymptotic for large momentum to the result implied by the asymptotic freedom and the renormalization group: This fundamental constraint fixes asymptotically the residues of the poles of the propagators in terms of the mass spectrum and of the anomalous dimensions of the local operators. For the mass gap problem, in the search of a hyperfinite subalgebra containing the scalar sector of large-N YM, a major role is played by the existence of a TFT underlying the large-N limit of YM, with twisted boundary conditions on a torus or, which is the same by Morita duality, on a noncommutative torus. The TFT is trivial at the leading large-N order and localized on a set of critical points by means of a quantum version of Morse–Smale–Floer homology, that involves loop equations in the ASD variables. A hyperfinite sector arises by fluctuations around the trivial TFT, in which the joint spectrum of scalar and pseudoscalar glueballs is linear in the square of the masses [Formula: see text] with degeneracy k = 1, 2,…, and the two-point correlator satisfies the aforementioned fundamental constraint arising by the asymptotic freedom and the renormalization group.

scholarly journals Unattainability of the trans-Planckian regime in nonlocal quantum gravity

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
F. Briscese ◽  
L. Modesto
Keyword(s):  
Quantum Gravity ◽  
Laboratory Experiments ◽  
Field Theories ◽  
Asymptotic Freedom ◽  
Particle Accelerators ◽  
Energy Regime ◽  
Cosmological Problem ◽  
Nonlocal Quantum ◽  
Nonlocal Field ◽  
Elegant Solution

Abstract Based on the ultraviolet asymptotic freedom of nonlocal quantum gravity, we show that the trans-Planckian energy regime is unattainable in laboratory experiments. As physical implications, it turns out that the violation of causality, typical of nonlocal field theories, can never be detected in particle accelerators, while the asymptotic freedom of the theory provides an elegant solution to the so called trans-Planckian cosmological problem.

Conformal invariance and asymptotic freedom in quantum gravity

1978 ◽  
Vol 77 (3) ◽  
pp. 262-266 ◽  
Author(s):  
E.S. Fradkin ◽  
G.A. Vilkovisky
Keyword(s):  
Quantum Gravity ◽  
Conformal Invariance ◽  
Asymptotic Freedom
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