Infrared Yang–Mills theory: A renormalization group perspective

2016 ◽  
Vol 25 (07) ◽  
pp. 1642002 ◽  
Author(s):  
Axel Weber ◽  
Pietro Dall’Olio ◽  
Francisco Astorga
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Analytical Approach ◽  
Landau Gauge ◽  
Momentum Dependence ◽  
Lattice Data ◽  
Four Dimensions ◽  
Yang Mills ◽  
Epsilon Expansion ◽  
Renormalization Group Equations

We describe a technically very simple analytical approach to the deep infrared regime of Yang–Mills theory in the Landau gauge via Callan–Symanzik renormalization group equations in an epsilon expansion. This approach recovers all the solutions for the infrared gluon and ghost propagators previously found by solving the Dyson–Schwinger equations of the theory and singles out the solution with decoupling behavior, confirmed by lattice calculations, as the only one corresponding to an infrared attractive fixed point (for space-time dimensions above two). For the case of four dimensions, we describe the crossover of the system from the ultraviolet to the infrared fixed point and determine the complete momentum dependence of the propagators. The results for different renormalization schemes are compared to the lattice data.

scholarly journals WHAT THE INFRARED BEHAVIOR OF QCD VERTEX FUNCTIONS IN LANDAU GAUGE CAN TELL US ABOUT CONFINEMENT

2007 ◽  
Vol 16 (09) ◽  
pp. 2720-2732 ◽  
Author(s):  
R. ALKOFER ◽  
C. S. FISCHER ◽  
F. J. LLANES-ESTRADA ◽  
K. SCHWENZER
Keyword(s):  
Renormalization Group ◽  
Chiral Symmetry ◽  
Gluon Propagator ◽  
Landau Gauge ◽  
Quark Propagator ◽  
Lattice Data ◽  
Gluon Vertex ◽  
Infrared Behavior ◽  
Renormalization Group Equations ◽  
Infrared Singularities

The infrared behavior of Landau gauge QCD vertex functions is investigated employing a skeleton expansion of the Dyson–Schwinger and Renormalization Group equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon vertex functions are presented. Positivity violation of the gluon propagator, and thus gluon confinement, is demonstrated. Results of the Dyson–Schwinger equations for a finite volume are compared to corresponding lattice data. It is analytically demonstrated that a linear rising potential between heavy quarks can be generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities necessarily entails the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken, either explicitly or dynamically.

scholarly journals COSMOLOGICAL PERTURBATIONS IN RENORMALIZATION GROUP DERIVED COSMOLOGIES

2004 ◽  
Vol 13 (01) ◽  
pp. 107-121 ◽  
Author(s):  
A. BONANNO ◽  
M. REUTER
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Matter Density ◽  
Explicit Solutions ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Covariant Approach ◽  
Cosmological Perturbation Theory ◽  
Spatial Gradients ◽  
Renormalization Group Equations

A linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid Universe with dynamically evolving Newton constant G and cosmological constant Λ is presented. A gauge invariant formalism is developed by means of the covariant approach, and the acoustic propagation equations governing the evolution of the comoving fractional spatial gradients of the matter density, G, and Λ are thus obtained. Explicit solutions are discussed in cosmologies where both G and Λ vary according to renormalization group equations in the vicinity of a fixed point.

THE RENORMALIZATION OF THE NON-RENORMALIZABLE FOUR-DIMENSIONAL FOUR-FERMION INTERACTION

1993 ◽  
Vol 08 (09) ◽  
pp. 797-802 ◽  
Author(s):  
N.V. KRASNIKOV
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Scalar Fields ◽  
Renormalization Group Equations ◽  
Point Solution ◽  
Renormalizable Theory

We show that the non-renormalizable four-dimensional four-fermion Nambu interaction of color quarks can be renormalized. The non-renormalizable four-fermion interaction of color quarks is equivalent to the special (fixed-point) solution of the renormalization group equations for the renormalizable theory describing the interaction of the scalar fields with color quarks.

scholarly journals QUANTUM DILATONIC GRAVITY IN d=2,4 AND 5 DIMENSIONS

2001 ◽  
Vol 16 (06) ◽  
pp. 1015-1108 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV
Keyword(s):  
Black Hole ◽  
Effective Action ◽  
Gauge Coupling ◽  
Conformal Anomaly ◽  
De Sitter ◽  
Nonzero Temperature ◽  
Four Dimensions ◽  
Yang Mills ◽  
Renormalization Group Equations ◽  
The One

We review (mainly) quantum effects in the theories where the gravity sector is described by metric and dilaton. The one-loop effective action for dilatonic gravity in two and four dimensions is evaluated. Renormalization group equations are constructed. The conformal anomaly and induced effective action for 2d and 4d dilaton coupled theories are found. It is applied to the study of quantum aspects of black hole thermodynamics, like calculation of Hawking radiation and quantum corrections to black hole parameters and investigation of quantum instability for such objects with multiple horizons. The use of the above effective action in the construction of nonsingular cosmological models in Einstein or Brans–Dicke (super)gravity and investigation of induced wormholes in supersymmetric Yang–Mills theory are given.5d dilatonic gravity (bosonic sector of compactified IIB supergravity) is discussed in connection with bulk/boundary (or AdS/CFT) correspondence. Running gauge coupling and quark–antiquark potential for boundary gauge theory at zero or nonzero temperature are calculated from d=5 dilatonic anti-de Sitter-like background solution which represents anti-de Sitter black hole for periodic time.

LONG DISTANCE DYNAMICS AND CONFINEMENT VIA RG DECIMATIONS

2009 ◽  
Vol 24 (34) ◽  
pp. 2717-2730 ◽  
Author(s):  
E. T. TOMBOULIS
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Upper And Lower Bounds ◽  
Free Energies ◽  
Long Distance ◽  
Strongly Coupled ◽  
Four Dimensions ◽  
Lattice Regularization

We review a recently developed framework employing computable Renormalization Group (RG) decimations for gauge theories in the lattice regularization. They provide upper and lower bounds at every scale for free energies and some order parameters. By interpolating between these bounds representations of the exact quantities are obtained at progressively longer scales (coarser lattices). In the case of the SU(2) gauge theory in four dimensions RG flow to the confining strongly coupled regime is obtained for any initial coupling; whereas for the U(1) theory a fixed point is reached for small initial coupling.

scholarly journals THE RENORMALIZATION STRUCTURE AND QUANTUM EQUIVALENCE OF 2D DILATON GRAVITIES

1994 ◽  
Vol 09 (06) ◽  
pp. 933-951 ◽  
Author(s):  
E. ELIZALDE ◽  
S. D. ODINTSOV ◽  
S. NAFTULIN
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Effective Action ◽  
Quantum Level ◽  
Dilaton Field ◽  
Dilaton Gravity ◽  
Specific Calculation ◽  
Equivalent Quantum ◽  
Renormalization Group Equations ◽  
The One

The one-loop effective action corresponding to the general model of dilaton gravity given by the Lagrangian [Formula: see text], where Z (Φ), C (Φ) and V (Φ) are arbitrary functions of the dilaton field, is found. The question of the quantum equivalence of classically equivalent dilaton gravities is studied. By specific calculation of explicit examples, it is shown that classically equivalent quantum gravities are also perturbatively equivalent at the quantum level, but only on-shell. The renormalization group equations for the generalized effective couplings Z (Φ), C (Φ) and V (Φ) are written. An analysis of the equations shows, in particular, that the gravitational sector of the Callan–Giddings–Harvey–Strominger model is not a fixed point of these equations.

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