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.

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.

The renormalization group in perturbative quantum gravity

2021 ◽  
pp. 488-493
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Renormalization Group ◽  
Quantum Gravity ◽  
Minimal Subtraction Scheme ◽  
Loop Approximation ◽  
Renormalization Group Equations ◽  
Gauge Fixing ◽  
Perturbative Renormalization ◽  
Fourth Derivative ◽  
Perturbative Quantum ◽  
The One

This is a short chapter summarizing the main results concerning the renormalization group in models of pure quantum gravity, without matter fields. The chapter starts with a critical analysis of non-perturbative renormalization group approaches, such as the asymptotic safety hypothesis. After that, it presents solid one-loop results based on the minimal subtraction scheme in the one-loop approximation. The polynomial models that are briefly reviewed include the on-shell renormalization group in quantum general relativity, and renormalization group equations in fourth-derivative quantum gravity and superrenormalizable models. Special attention is paid to the gauge-fixing dependence of the renormalization group trajectories.

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.

scholarly journals 2D QUANTUM GRAVITY COUPLED TO RENORMALIZABLE MATTER FIELDS

1994 ◽  
Vol 09 (32) ◽  
pp. 5689-5709 ◽  
Author(s):  
JAN AMBJØRN ◽  
KAZUO GHOROKU
Keyword(s):  
Renormalization Group ◽  
Quantum Gravity ◽  
Effective Action ◽  
Two Dimensional ◽  
Conformally Invariant ◽  
Renormalization Group Equations ◽  
Β Function ◽  
Matter Fields

We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable but not conformally invariant. Questions concerning the β function and the effective action are addressed, and the effective action and the dressed renormalization group equations are determined for various matter potentials.

THE ASYMPTOTICALLY FREE AND ASYMPTOTICALLY CONFORMALLY INVARIANT GRAND UNIFICATION THEORIES IN CURVED SPACE-TIME

1990 ◽  
Vol 05 (20) ◽  
pp. 1599-1604 ◽  
Author(s):  
I.L. BUCHBINDER ◽  
I.L. SHAPIRO ◽  
E.G. YAGUNOV
Keyword(s):  
Renormalization Group ◽  
Gravitational Field ◽  
Gauge Group ◽  
Flat Space ◽  
Space Time ◽  
Grand Unification ◽  
Curved Space ◽  
Conformally Invariant ◽  
Renormalization Group Equations ◽  
The One

GUT’s in curved space-time is considered. The set of asymptotically free and asymptotically conformally invariant models based on the SU (N) gauge group is constructed. The general solutions of renormalization group equations are considered as the special ones. Several SU (2N) models, which are finite in flat space-time (on the one-loop level) and asymptotically conformally invariant in external gravitational field are also presented.

DISORDER-INDUCED INSTABILITY OF THE QUANTUM CRITICAL BEHAVIOR OF BOSE FLUIDS

2000 ◽  
Vol 14 (05) ◽  
pp. 173-179
Author(s):  
I. P. TAKOV
Keyword(s):  
Renormalization Group ◽  
Critical Behavior ◽  
Short Range ◽  
Zero Temperature ◽  
Classical Systems ◽  
Renormalization Group Equations ◽  
Quantum Critical ◽  
The One ◽  
Quantum Critical Behavior ◽  
Short Range Correlations

The one-loop renormalization-group equations for Bose fluids with randomly distributed impurities are derived and analyzed with the help of a double ∊-expansion. While the low temperature critical behavior is similar to that of classical systems with extended impurities, the proper quantum critical behavior of disordered Bose fluids at zero temperature is unstable with respect to randomly distributed impurities with short-range correlations.

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 The renormalization group and the effective action

2011 ◽  
Vol 89 (3) ◽  
pp. 277-280 ◽  
Author(s):  
D. G.C. McKeon
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Gauge Field ◽  
Effective Potential ◽  
Effective Action ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
The One ◽  
External Gauge

The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function β, the next-to-leading-log (NLL) contributions in terms of the two-loop RG function, etc. The log-independent pieces are not determined by the RG equation, but can be fixed by considering the anomaly in the trace of the energy-momentum tensor. Similar considerations can be applied to the effective potential V for a scalar field [Formula: see text]; here the log-independent pieces are fixed by the condition [Formula: see text].

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.

Sign in / Sign up

Export Citation Format

Share Document