Singularity structure of maximally supersymmetric scattering amplitudes

Area of Science:

• High-energy physics
• Quantum field theory
• Supersymmetry

Background:

• The study of scattering amplitudes in quantum field theories is crucial for understanding fundamental interactions.
• Maximally supersymmetric Yang-Mills theory (N=4 SYM) is a key theoretical laboratory due to its rich mathematical structure and potential connections to other theories.
• Understanding the behavior of amplitudes beyond the planar limit is essential for a complete picture.

Purpose of the Study:

• To investigate the properties of loop amplitudes in N=4 SYM beyond the planar limit.
• To determine if non-planar amplitudes share the remarkable structures observed in planar N=4 SYM.
• To explore the implications of these findings for maximal supergravity (N=8 SUGRA).

Main Methods:

• Calculation of four-particle scattering amplitudes in N=4 SYM up to two-loop order.
• Analysis of the singularity structure of these amplitudes, specifically looking for logarithmic singularities and poles at infinity.
• Comparison of the calculated amplitudes with known properties of the planar theory, such as uniform transcendentality.

Main Results:

• Evidence presented suggests that loop amplitudes in full N=4 SYM beyond the planar limit share structures with the planar theory.
• Specifically, the four-particle amplitude at two loops exhibits only logarithmic singularities.
• The amplitude is also found to be free of poles at infinity, consistent with uniform transcendentality and UV finiteness.

Conclusions:

• The findings indicate that the remarkable structures of planar N=4 SYM persist beyond the planar limit, at least up to two loops.
• These properties are closely linked to uniform transcendentality and the ultraviolet (UV) finiteness of the theory.
• The results have potential implications for understanding the structure of maximal supergravity (N=8 SUGRA).