scholarly journals The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge

2017 ◽  
Vol 2017 (10) ◽  
Author(s):  
Thomas Luthe ◽  
Andreas Maier ◽  
Peter Marquard ◽  
York Schröder
Keyword(s):  
Gauge Group ◽  
Beta Function ◽  
Feynman Gauge ◽  
Anomalous Dimensions ◽  
General Gauge

scholarly journals The Five-loop Beta Function for a General Gauge Group

2017 ◽  
Vol 48 (12) ◽  
pp. 2331
Author(s):  
T. Luthe ◽  
A. Maier ◽  
P. Marquard ◽  
Y. Schröder
Keyword(s):  
Gauge Group ◽  
Beta Function ◽  
General Gauge

scholarly journals Five-loop quark mass and field anomalous dimensions for a general gauge group

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Thomas Luthe ◽  
Andreas Maier ◽  
Peter Marquard ◽  
York Schröder
Keyword(s):  
Gauge Group ◽  
Quark Mass ◽  
Anomalous Dimensions ◽  
General Gauge

scholarly journals Towards the five-loop Beta function for a general gauge group

2016 ◽  
Vol 2016 (7) ◽  
Author(s):  
Thomas Luthe ◽  
Andreas Maier ◽  
Peter Marquard ◽  
York Schröder
Keyword(s):  
Gauge Group ◽  
Beta Function ◽  
General Gauge

scholarly journals CONFORMAL HOUSE

2010 ◽  
Vol 25 (24) ◽  
pp. 4603-4621 ◽  
Author(s):  
THOMAS A. RYTTOV ◽  
FRANCESCO SANNINO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Gauge Group ◽  
Gauge Theories ◽  
Simultaneous Presence ◽  
Consistency Check ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Mass Terms

We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

ASYMPTOTICS OF THE ALTARELLI-PARISI-LIPATOV EVOLUTION KERNELS OF PARTON DISTRIBUTIONS

1989 ◽  
Vol 04 (13) ◽  
pp. 1257-1276 ◽  
Author(s):  
G.P. KORCHEMSKY
Keyword(s):  
Gauge Group ◽  
Perturbative Qcd ◽  
Anomalous Dimension ◽  
Beta Function ◽  
Simple Equation ◽  
Parton Distributions ◽  
Axial Gauge ◽  
Quark Field ◽  
Cusp Anomalous Dimension

The asymptotics of the evolution kernels Pab(z) of parton distributions is investigated as z→1. It is proven that to all orders of perturbative QCD, [Formula: see text] where [Formula: see text] is the cusp anomalous dimension of the contour functionals in the fundamental (α=“quark”) and adjoint (α=“gluon”) representations of gauge group and, to the lowest orders, Cα are related to the anomalous dimension of a quark field in the axial gauge and the beta function of QCD by a simple equation.

scholarly journals The all-loop perturbative derivation of the NSVZ $$\beta $$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
K. V. Stepanyantz
Keyword(s):  
Renormalization Group ◽  
Beta Function ◽  
Covariant Derivatives ◽  
Anomalous Dimensions ◽  
Higher Covariant Derivative ◽  
Higher Covariant Derivatives ◽  
Loop Approximation ◽  
Abelian Case ◽  
Group Functions ◽  
Supersymmetric Gauge

AbstractThe perturbative all-loop derivation of the NSVZ $$\beta $$ β -function for $${{\mathcal {N}}}=1$$ N = 1 supersymmetric gauge theories regularized by higher covariant derivatives is finalized by calculating the sum of singularities produced by quantum superfields. These singularities originate from integrals of double total derivatives and determine all contributions to the $$\beta $$ β -function starting from the two-loop approximation. Their sum is expressed in terms of the anomalous dimensions of the quantum gauge superfield, of the Faddeev–Popov ghosts, and of the matter superfields. This allows obtaining the NSVZ equation in the form of a relation between the $$\beta $$ β -function and these anomalous dimensions for the renormalization group functions defined in terms of the bare couplings. It holds for an arbitrary renormalization prescription supplementing the higher covariant derivative regularization. For the renormalization group functions defined in terms of the renormalized couplings we prove that in all loops one of the NSVZ schemes is given by the HD + MSL prescription.

scholarly journals Three-loop contribution of the Faddeev–Popov ghosts to the $$\beta $$-function of $$\mathcal{N}=1$$ supersymmetric gauge theories and the NSVZ relation

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
M. D. Kuzmichev ◽  
N. P. Meshcheriakov ◽  
S. V. Novgorodtsev ◽  
I. E. Shirokov ◽  
K. V. Stepanyantz
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Beta Function ◽  
Supersymmetric Gauge Theories ◽  
Loop Contribution ◽  
Covariant Derivatives ◽  
Anomalous Dimensions ◽  
Higher Covariant Derivatives ◽  
Supersymmetric Gauge ◽  
Multiloop Calculations

Abstract We find the three-loop contribution to the $$\beta $$β-function of $$\mathcal{N}=1$$N=1 supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev–Popov ghosts. This is done using a recently proposed algorithm, which essentially simplifies such multiloop calculations. The result is presented in the form of an integral of double total derivatives in the momentum space. The considered contribution to the $$\beta $$β-function is compared with the two-loop anomalous dimension of the Faddeev–Popov ghosts. This allows verifying the validity of the NSVZ equation written as a relation between the $$\beta $$β-function and the anomalous dimensions of the quantum superfields. It is demonstrated that in the considered approximation the NSVZ equation is satisfied for the renormalization group functions defined in terms of the bare couplings. The necessity of the nonlinear renormalization for the quantum gauge superfield is also confirmed.

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