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Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
Rutger H Boels1, Tobias Huber2, Gang Yang3
1II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany.
Physical Review Letters
|December 9, 2017
Summary
The lightlike cusp anomalous dimension, crucial for gauge theories, was calculated to four loops. This study reveals a breakdown in quadratic Casimir scaling at this loop order, a novel finding from numerical Sudakov form factor computations.
Area of Science:
- High-energy physics
- Quantum field theory
- Supersymmetric Yang-Mills theory
Background:
- The lightlike cusp anomalous dimension is a universal function governing infrared divergences in gauge theories.
- Integrability fully determines this dimension in maximally supersymmetric Yang-Mills theory up to three loops.
Purpose of the Study:
- To compute the lightlike cusp anomalous dimension at the four-loop order.
- To investigate the appearance of nonplanar corrections and their impact on theoretical scaling properties.
Main Methods:
- Numerical computation of the Sudakov form factor.
- Application of methods to manage number-theoretic aspects of integrals.
Main Results:
- The four-loop nonplanar correction to the lightlike cusp anomalous dimension was obtained for the first time.
- Explicit demonstration that quadratic Casimir scaling breaks down at four loops.
Conclusions:
- The breakdown of quadratic Casimir scaling at four loops is a significant deviation from lower-loop behavior.
- This finding advances the understanding of nonplanar effects in supersymmetric gauge theories.
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