Antipodal Self-Duality for a Four-Particle Form Factor.

Area of Science:

• Theoretical physics
• High-energy physics
• Quantum field theory

Background:

• Planar N=4 super-Yang-Mills theory is a crucial model in theoretical physics.
• Understanding its properties, like form factors, is essential for advancements.
• Previous studies hinted at dualities within this theory.

Purpose of the Study:

• To bootstrap the symbol of the maximal-helicity-violating four-particle form factor.
• To analyze its properties, including Steinmann relations and potential dualities.
• To connect findings with existing dualities in the theory.

Main Methods:

• Symbol bootstrapping techniques were employed.
• Minimal normalization was applied to the symbol.
• Analysis of the remainder function for antipodal self-duality was performed.

Main Results:

• The symbol for the specific form factor was successfully bootstrapped.
• It was found to contain only 34 letters and obey extended Steinmann relations.
• An antipodal self-duality was discovered in the remainder function.

Conclusions:

• The bootstrapped symbol and its properties provide new insights into planar N=4 super-Yang-Mills theory.
• The observed antipodal self-duality implies a deeper connection between different scattering amplitudes and form factors.
• This work contributes to the understanding of symmetries and structures in quantum field theories.