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

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 The UV fate of anomalous U(1)s and the Swampland

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Nathaniel Craig ◽  
Isabel Garcia Garcia ◽  
Graham D. Kribs
Keyword(s):  
Quantum Gravity ◽  
Gauge Theories ◽  
Critical Size ◽  
Gauge Coupling ◽  
Low Energy ◽  
Gravitational Anomaly ◽  
Light Vector ◽  
Energy Theory ◽  
The Cost ◽  
Weak Gravity

Abstract Massive U(1) gauge theories featuring parametrically light vectors are suspected to belong in the Swampland of consistent EFTs that cannot be embedded into a theory of quantum gravity. We study four-dimensional, chiral U(1) gauge theories that appear anomalous over a range of energies up to the scale of anomaly-cancelling massive chiral fermions. We show that such theories must be UV-completed at a finite cutoff below which a radial mode must appear, and cannot be decoupled — a Stückelberg limit does not exist. When the infrared fermion spectrum contains a mixed U(1)-gravitational anomaly, this class of theories provides a toy model of a boundary into the Swampland, for sufficiently small values of the vector mass. In this context, we show that the limit of a parametrically light vector comes at the cost of a quantum gravity scale that lies parametrically below MP1, and our result provides field theoretic evidence for the existence of a Swampland of EFTs that is disconnected from the subset of theories compatible with a gravitational UV-completion. Moreover, when the low energy theory also contains a U(1)3 anomaly, the Weak Gravity Conjecture scale makes an appearance in the form of a quantum gravity cutoff for values of the gauge coupling above a certain critical size.

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

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

scholarly journals Possible Explanation of the Quark Confinement and Asymptotic Freedom, and Possible Solution to the Yang-Mills Mass Gap Problem

2019 ◽  
Vol 16 (1) ◽  
pp. 391-478
Author(s):  
Antonio Puccini
Keyword(s):  
Gauge Theories ◽  
Rest Mass ◽  
Mathematical Structure ◽  
Physical Reality ◽  
Asymptotic Freedom ◽  
Nuclear Forces ◽  
Spatial Confinement ◽  
Yang Mills ◽  
Mass Gap ◽  
Narrow Space

With this work, we try to answer 3 fundamental questions that have plagued mathematicians and physicists for several decades. As known, the spontaneous symmetry breaking (SSB) and the Brout-Englert-Higgs Mechanism (BEH-M) solved the Yang-Mills Mass Gap Problem. However, various mathematicians, even prestigious ones, consider the basic assumptions of the gauge theories to be wrong, as well as in conflict with the experimental evidences and in clear disagreement with the facts, distorcing the physical reality itself. Likewise, the Quantum Fields Theory (QFT) is mathematically inconsistent, adopting a mathematical structure somewhat complicated and arbitrary, which does not satisfy the strong demands for coherence. The weakest point of the gauge theories, in our opinion, consists in imposing that all the particles must be free of an intrinsic mass (massless). On the contrary, even for the particle considered universally massless, i.e. the photon (P), our calculations show a dynamic-mass, a push-momentum (p) of 1.325⋅10−22[g⋅cm/s]. That is, an optic P hits a particle with an energy-mass greater than 100 protons rest-mass’. It is clear that if we replaced this value with the full value of the P inserted in the equations of the Perturbation Theory, QFT and Yang-Mills theories, all divergences, that is all zeroes and infinities, would suddenly disappear. Consequently, the limits imposed by the SSB disappear so that there is no longer any need to deny the mass to the Nuclear Forces bosons, including the Yang-Mills b quantum. Still, the photons (Ps) are the basis of the quantum vacuum energy, which is distributed ubiquitously, also within the intra-atomic spaces. It is likely that a lot of Ps were trapped in atomic nuclei (at the time of nucleosynthesis) and among quarks (Qs) at the time of primordial nucleonic synthesis. We believe that when Qs get too close to each other, till repelling each other (Asymptotic Freedom of Qs), this may depend on the presence of a multitude of Ps that, no further compressible, begin to exert an antigravity repulsive force, just as a Dark Energy. This limit to Compressibility (C) of the radiation is shown in equation: PV 4/3 = C, where V is the volume, and P is the Pressure of the photonic gas. Quantum Mechanics plays a crucial role, through the Uncertainty Principle, in the spatial Confinement of Qs, which have remained eternally confined in an extremely narrow space by the  Strong Interaction, but in primis by the very short range (likely ≈8.44[±1.44]⋅10-16cm) and lifetime of gluon(G) which, from our calculations, is ≈2.73[±0.564]⋅10-26 sec. Therefore, a new parameter may be added to the Qs and G spatial Confinement: the b quantum or G Temporal Confinement (and of their Colours and anti-Colours). 

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

scholarly journals MULTI-PLAQUETTE SOLUTIONS FOR DISCRETIZED ASHTEKAR GRAVITY

1996 ◽  
Vol 11 (05) ◽  
pp. 349-356 ◽  
Author(s):  
KIYOSHI EZAWA
Keyword(s):  
Quantum Gravity ◽  
Heat Kernel ◽  
Gauge Theories ◽  
Hamiltonian Constraint ◽  
Spin Network ◽  
Connected Set ◽  
Network States ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

A discretized version of canonical quantum gravity proposed by Loll is investigated. After slightly modifying Loll’s discretized Hamiltonian constraint, we encode its action on the spin network states in terms of combinatorial topological manipulations of the lattice loops. Using this topological formulation we find new solutions to the discretized Wheeler-DeWitt equation. These solutions have their support on the connected set of plaquettes. We also show that these solutions are not normalizable with respect to the induced heat-kernel measure on SL(2, C) gauge theories.

Eigenvalue conditions and asymptotic freedom ofSO(N)gauge theories

1978 ◽  
Vol 18 (12) ◽  
pp. 4721-4725 ◽  
Author(s):  
Ngee-Pong Chang ◽  
J. Perez-Mercader
Keyword(s):  
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
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