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 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

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 Large $$N_\mathrm{f}$$ for multiple representations

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Giacomo Cacciapaglia ◽  
Shahram Vatani
Keyword(s):  
Fixed Point ◽  
Gauge Group ◽  
Gauge Theories ◽  
Beta Function ◽  
Multiple Representations ◽  
Abelian Gauge ◽  
Pole Structure

AbstractWe present an extension of the large-$$N_\mathrm{f}$$ N f formalism that allows one to study cases with multiple fermion representations. The pole structure in the beta function is traced back to the intrinsic non-abelian nature of the gauge group, independently from the fermion representation. This result validates the conjectured existence of an interactive UV fixed point for non-abelian gauge theories with large fermion multiplicity. Finally, we apply our results to chiral gauge theories.

scholarly journals Modular invariant holographic correlators for $$ \mathcal{N} $$ = 4 SYM with general gauge group

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Luis F. Alday ◽  
Shai M. Chester ◽  
Tobias Hansen
Keyword(s):  
Gauge Group ◽  
Flat Space ◽  
Closed Form Expression ◽  
Tree Level ◽  
Modular Invariant ◽  
Higher Derivative ◽  
S Matrix ◽  
Space Limit ◽  
Type Iib String Theory ◽  
General Gauge

Abstract We study the stress tensor four-point function for $$ \mathcal{N} $$ N = 4 SYM with gauge group G = SU(N), SO(2N + 1), SO(2N) or USp(2N) at large N . When G = SU(N), the theory is dual to type IIB string theory on AdS5× S5 with complexified string coupling τs, while for the other cases it is dual to the orbifold theory on AdS5× S5/ℤ2. In all cases we use the analytic bootstrap and constraints from localization to compute 1-loop and higher derivative tree level corrections to the leading supergravity approximation of the correlator. We give perturbative evidence that the localization constraint in the large N and finite complexified coupling τ limit can be written for each G in terms of Eisenstein series that are modular invariant in terms of τs ∝ τ, which allows us to fix protected terms in the correlator in that limit. In all cases, we find that the flat space limit of the correlator precisely matches the type IIB S-matrix. We also find a closed form expression for the SU(N) 1-loop Mellin amplitude with supergravity vertices. Finally, we compare our analytic predictions at large N and finite τ to bounds from the numerical bootstrap in the large N regime, and find that they are not saturated for any G and any τ , which suggests that no physical theory saturates these bootstrap bounds.

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