Harmonic R matrices for scattering amplitudes and spectral regularization.

Area of Science:

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

Background:

• Planar N=4 supersymmetric Yang-Mills theory is known to be integrable.
• Integrability has not been directly applicable to calculating scattering amplitudes.
• Existing methods like dimensional regularization have limitations.

Purpose of the Study:

• To develop a method for utilizing integrability in scattering amplitude calculations.
• To introduce a spectral parameter deformation for scattering amplitudes.
• To explore the potential of this deformation as a novel regularization technique.

Main Methods:

• Deforming all scattering amplitudes by a spectral parameter.
• Analyzing the deformed tree-level four-point function.
• Examining deformed on-shell three-point functions.
• Investigating the spectral parameter as a symmetry-respecting regulator.

Main Results:

• The deformed tree-level four-point function corresponds to the one-loop R matrix of the integrable N=4 spin chain.
• Deformed three-point functions yield new three-leg R matrices satisfying bootstrap equations.
• Initial evidence suggests the spectral parameter can replace dimensional regularization.

Conclusions:

• The spectral parameter deformation provides a novel link between integrability and scattering amplitudes.
• This deformation leads to new mathematical structures (R matrices) in the theory.
• The spectral parameter shows promise as a new, symmetry-respecting regularization method for quantum field theories.