scholarly journals A MANIFESTLY GAUGE INVARIANT AND UNIVERSAL CALCULUS FORSU(N) YANG–MILLS

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4627-4761 ◽  
Author(s):  
OLIVER J. ROSTEN
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Explicit Dependence ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Group A ◽  
Β Function ◽  
Exact Renormalization Group

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU (N) Yang–Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the β function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these nonuniversal contributions is done in an entirely diagrammatic fashion.

scholarly journals A GAUGE INVARIANT REGULATOR FOR THE ERG

2001 ◽  
Vol 16 (11) ◽  
pp. 1989-2001 ◽  
Author(s):  
S. ARNONE ◽  
YU. A. KUBYSHIN ◽  
T. R. MORRIS ◽  
J. F. TIGHE
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Ultra Violet ◽  
Group Approach ◽  
Gauge Invariant ◽  
Four Dimensions ◽  
Yang Mills ◽  
Renormalization Group Approach ◽  
Higher Derivatives ◽  
Exact Renormalization Group

A gauge invariant regularisation for dealing with pure Yang-Mills theories within the exact renormalization group approach is proposed. It is based on the regularisation via covariant higher derivatives and includes auxiliary Pauli-Villars fields which amounts to a spontaneously broken SU(N|N) super-gauge theory. We demonstrate perturbatively that the extended theory is ultra-violet finite in four dimensions and argue that it has a sensible limit when the regularization cutoff is removed.

The effect of renormalization in a finite massive theory

1995 ◽  
Vol 73 (9-10) ◽  
pp. 615-618
Author(s):  
D. G. C. McKeon
Keyword(s):  
Renormalization Group ◽  
Pole Mass ◽  
Coupling Constant ◽  
Loop Order ◽  
Effective Coupling ◽  
Yang Mills ◽  
Effective Coupling Constant ◽  
Group A ◽  
Massive Theory ◽  
Β Function

The fact that a theory is finite does not preclude the possibility of making finite renormalizations. With this in mind, we consider massive N = 4 super Yang–Mills theory, a model known to have a vanishing β function and to be finite at one-loop order when one uses the formulation using N = 1 superfields. The mass that appears in the Lagrangian is not a pole of the propagator when radiative effects are included; we fix the position of this pole and then discuss how the effective coupling constant in the theory depends on this pole mass. This procedure is akin to the original Gell-Mann–Low approach to the renormalization group. A one-loop calculation indicates that the effective coupling vanishes as the pole mass goes to zero and diverges for large values of the pole mass.

MASSIVE AXIAL GAUGE IN THE EXACT RENORMALIZATION GROUP APPROACH

2001 ◽  
Vol 16 (11) ◽  
pp. 2101-2104 ◽  
Author(s):  
P. PANZA ◽  
R. SOLDATI
Keyword(s):  
Renormalization Group ◽  
Wilson Loop ◽  
Gauge Theories ◽  
Massless Limit ◽  
Group Approach ◽  
Gauge Invariant ◽  
Axial Gauge ◽  
Renormalization Group Approach ◽  
Exact Renormalization Group

The Exact Renormalization Group (ERG) approach to massive gauge theories in the axial gauge is studied and the smoothness of the massless limit is analysed for a formally gauge invariant quantity such as the Euclidean Wilson loop.

scholarly journals LOOP VARIABLES IN STRING THEORY

2003 ◽  
Vol 18 (05) ◽  
pp. 767-809 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Equations Of Motion ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
World Sheet ◽  
Gauge Invariant ◽  
Variable Approach ◽  
Exact Renormalization Group

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space–time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

scholarly journals Exact Renormalization Group Approach in Scalar and Fermionic Theories

1998 ◽  
Vol 12 (12n13) ◽  
pp. 1321-1341 ◽  
Author(s):  
Yu. Kubyshin
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Derivative Expansion ◽  
Group Approach ◽  
Renormalization Group Approach ◽  
Exact Renormalization Group

The Polchinski version of the exact renormalization group equation is discussed and its applications in scalar and fermionic theories are reviewed. Relation between this approach and the standard renormalization group is studied, in particular the relation between the derivative expansion and the perturbation theory expansion is worked out in some detail.

scholarly journals EXACT RENORMALIZATION GROUP IN ALGEBRAIC NONCOVARIANT GAUGES

2001 ◽  
Vol 16 (11) ◽  
pp. 2125-2130
Author(s):  
M. SIMIONATO
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Light Cone ◽  
Wilson Loop ◽  
Gauge Theories ◽  
Mass Term ◽  
Abelian Gauge ◽  
Light Cone Gauge ◽  
Infrared Limit ◽  
Exact Renormalization Group

I study a class of Wilsonian formulations of non-Abelian gauge theories in algebraic noncovariant gauges where the Wilsonian infrared cutoff Λ is inserted as a mass term for the propagating fields. In this way the Ward-Takahashi identities are preserved to all scales. Nevertheless the BRS-invariance in broken and the theory is gauge-dependent and unphysical at Λ≠ 0. Then I discuss the infrared limit Λ→0. I show that the singularities of the axial gauge choice are avoided in planar gauge and in light-cone gauge. Finally the rectangular Wilson loop of size 2L×2T is evaluated at lowest order in perturbation theory and a noncommutativity between the limits Λ→0 and T→∞ is pointed out.

scholarly journals Einstein–Yang–Mills theory: gauge invariant charges and linearization instability

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Emel Altas ◽  
Ercan Kilicarslan ◽  
Bayram Tekin
Keyword(s):  
General Relativity ◽  
Perturbation Theory ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Gauge Fields ◽  
Gauge Invariant ◽  
Yang Mills ◽  
First Order ◽  
Flat Spacetime ◽  
First Order Perturbation

AbstractWe construct the gauge-invariant electric and magnetic charges in Yang–Mills theory coupled to cosmological general relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser (Phys Lett B 116:259–263, 1982). For non-vanishing background gauge fields, the charges receive non-trivial contribution from the gravity part. In addition, we study the constraints on the first order perturbation theory and establish the conditions for linearization instability: that is the validity of the first order perturbation theory.

ON THE RENORMALIZATION GROUP FLOW IN N = 2 SUPERCONFORMAL MODELS

1990 ◽  
Vol 05 (27) ◽  
pp. 2261-2265 ◽  
Author(s):  
E. GAVA ◽  
M. STANISHKOV
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Renormalization Group Flow ◽  
Β Function ◽  
Group Flow ◽  
Chiral Superfield

We show that the β-function of N = 2 superconformal models perturbed by a slightly relevant chiral superfield does not have non-trivial IR fixed points to all orders in perturbation theory.

scholarly journals Gauge invariant perturbation theory via homotopy transfer

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Christoph Chiaffrino ◽  
Olaf Hohm ◽  
Allison F. Pinto
Keyword(s):  
Perturbation Theory ◽  
Lie Algebras ◽  
Closed String ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Cosmological Perturbation Theory ◽  
Invariant Perturbation Theory ◽  
General Gauge ◽  
Algorithmic Procedure

Abstract We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory. This is illustrated for Yang-Mills theory, gravity on flat and cosmological backgrounds and for the massless sector of closed string theory. The perturbation lemma yields an algorithmic procedure to determine the higher corrections of the gauge invariant variables and the action in terms of these.

Sign in / Sign up

Export Citation Format

Share Document