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The property of maximal transcendentality in the N=4 Supersymmetric Yang-Mills

A. V. Kotikov

TL;DR

This work investigates maximal transcendentality in $N=4$ SYM by focusing on the universal anomalous dimension $\gamma_{uni}(j)$ for twist-2 Wilson operators. It leverages the deep connection between BFKL and DGLAP dynamics, the integrable structure of the theory, and the Beisert-Eden-Staudacher framework to derive $\gamma_{uni}(j)$ up to four loops (and partial five-loop insights) using a combination of QCD results, master-integral techniques, and wrapping corrections. Detailed analyses of the limits $j\to 1$, $j\to 4$, and $j\to \infty$ illuminate the small-, Konishi-, and large-$j$ behavior, while AdS/CFT resummation and BES equations link weak- and strong-coupling regimes. The results provide strong tests for integrability-based approaches and support the consistent picture of scaling in the AdS/CFT correspondence.

Abstract

We present results for the universal anomalous dimension γ_{uni}(j) of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory in the first four orders of perturbation theory.

The property of maximal transcendentality in the N=4 Supersymmetric Yang-Mills

TL;DR

This work investigates maximal transcendentality in SYM by focusing on the universal anomalous dimension for twist-2 Wilson operators. It leverages the deep connection between BFKL and DGLAP dynamics, the integrable structure of the theory, and the Beisert-Eden-Staudacher framework to derive up to four loops (and partial five-loop insights) using a combination of QCD results, master-integral techniques, and wrapping corrections. Detailed analyses of the limits , , and illuminate the small-, Konishi-, and large- behavior, while AdS/CFT resummation and BES equations link weak- and strong-coupling regimes. The results provide strong tests for integrability-based approaches and support the consistent picture of scaling in the AdS/CFT correspondence.

Abstract

We present results for the universal anomalous dimension γ_{uni}(j) of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory in the first four orders of perturbation theory.

Paper Structure

This paper contains 14 sections, 55 equations.

Table of Contents

  1. Introduction
  2. Evolution equation in ${\mathcal{N}}=4$ SYM
  3. BFKL
  4. Leading order anomalous dimension matrix in ${\mathcal{N}}=4$ SYM
  5. Method of obtaining the eigenvalues of the anomalous dimension matrix in ${\mathcal{N}}=4$ SYM
  6. Calculation of Feynman integrals
  7. Universal anomalous dimension for ${\mathcal{N}}=4$ SYM
  8. The limit $j\rightarrow 1$
  9. The limit $j\rightarrow 4$
  10. The limit $j\rightarrow \infty$
  11. Resummation of $\gamma_{uni}$ and the AdS/CFT correspondence
  12. Beisert-Eden-Staudacher equation
  13. Bethe-ansatz and four-loop universal anomalous dimension
  14. Conclusion