Exact Off Shell Sudakov Form Factor in N=4 Supersymmetric Yang-Mills Theory

Area of Science:

• High-energy physics
• Quantum field theory
• Supersymmetric gauge theories

Background:

• The Sudakov form factor is crucial for understanding scattering amplitudes in quantum field theories.
• Planar N=4 supersymmetric Yang-Mills theory provides a tractable framework for studying non-perturbative effects.
• Investigating off-shell kinematics is essential for a complete description of physical processes.

Purpose of the Study:

• To analyze the Sudakov form factor in planar N=4 supersymmetric Yang-Mills theory in the off-shell regime.
• To investigate the exponentiation properties of both infrared-divergent and finite terms.
• To compare the results with existing theoretical conjectures and introduce a new relationship.

Main Methods:

• Consideration of the Coulomb branch to achieve off-shell kinematics.
• Perturbative calculations up to three loops.
• Comparison with the recently introduced null octagon within integrability-based approaches.

Main Results:

• Demonstration of exponentiation for both infrared-divergent and finite terms up to three loops.
• Identification of the octagon anomalous dimension (Γ_{oct}) as the coefficient of log^{2}(m^{2}).
• Observation that the logarithm of the Sudakov form factor equals twice the logarithm of the null octagon (O_{0}) up to three loops.

Conclusions:

• The exponentiation behavior observed contrasts with previous conjectures.
• The established relationship between the Sudakov form factor and the null octagon suggests a deeper connection.
• A conjecture is proposed for the all-loop order validity of this relationship, leveraging the known closed form of O_{0}.