scholarly journals Four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory

2007 ◽  
Vol 75 (8) ◽  
Author(s):  
Zvi Bern ◽  
Michael Czakon ◽  
Lance J. Dixon ◽  
David A. Kosower ◽  
Vladimir A. Smirnov
Keyword(s):  
Anomalous Dimension ◽  
Yang Mills ◽  
Cusp Anomalous Dimension

scholarly journals Eigenvalue spectrum and scaling dimension of lattice $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Georg Bergner ◽  
David Schaich
Keyword(s):  
Anomalous Dimension ◽  
Finite Lattice ◽  
Continuum Theory ◽  
Lattice Volume ◽  
Yang Mills ◽  
Lattice Regularization ◽  
Perturbative Renormalization ◽  
Zero Values ◽  
Definition Of ◽  
Group Flow

Abstract We investigate the lattice regularization of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory, by stochastically computing the eigenvalue mode number of the fermion operator. This provides important insight into the non-perturbative renormalization group flow of the lattice theory, through the definition of a scale-dependent effective mass anomalous dimension. While this anomalous dimension is expected to vanish in the conformal continuum theory, the finite lattice volume and lattice spacing generically lead to non-zero values, which we use to study the approach to the continuum limit. Our numerical results, comparing multiple lattice volumes, ’t Hooft couplings, and numbers of colors, confirm convergence towards the expected continuum result, while quantifying the increasing significance of lattice artifacts at larger couplings.

scholarly journals Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension

2016 ◽  
Vol 2016 (5) ◽  
Author(s):  
Marisa Bonini ◽  
Luca Griguolo ◽  
Michelangelo Preti ◽  
Domenico Seminara
Keyword(s):  
Anomalous Dimension ◽  
Cusp Anomalous Dimension

scholarly journals Three-loop cusp anomalous dimension and a conjecture for n loops

2016 ◽  
Vol 31 (13) ◽  
pp. 1650076 ◽  
Author(s):  
Nikolaos Kidonakis
Keyword(s):  
Top Quark ◽  
Anomalous Dimension ◽  
Numerical Results ◽  
Elementary Functions ◽  
Top Quark Production ◽  
Quark Production ◽  
Lower Loop ◽  
Analytical Expressions ◽  
Cusp Anomalous Dimension ◽  
Approximate Formulas

I present analytical expressions for the massive cusp anomalous dimension in QCD through three loops, first calculated in 2014, in terms of elementary functions and ordinary polylogarithms. I observe interesting relations between the results at different loops and provide a conjecture for the n-loop cusp anomalous dimension in terms of the lower-loop results. I also present numerical results and simple approximate formulas for the cusp anomalous dimension relevant to top-quark production.

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