Anomalous Dimensions from the N=4 Supersymmetric Yang-Mills Hexagon

Area of Science:

• High energy physics
• Quantum field theory
• String theory

Background:

• N=4 super Yang-Mills theory is a key model in quantum field theory with rich mathematical structure.
• Understanding operator dimensions is crucial for predicting physical observables.
• The su(2) sector simplifies complex theories while retaining important features.

Purpose of the Study:

• To compute the correlator of the Lagrange operator and two conjugate two-excitation operators.
• To investigate the su(2) sector of N=4 super Yang-Mills theory.
• To recover the planar one-loop anomalous dimension of renormalized operators.

Main Methods:

• Hexagon function computation
• Correlator analysis
• Renormalization techniques

Main Results:

• The correlator ⟨LKK[over ˜]⟩ was computed.
• The planar one-loop anomalous dimension was successfully recovered.
• The results are consistent with theoretical predictions for the su(2) sector.

Conclusions:

• Hexagon computations provide a powerful tool for studying N=4 super Yang-Mills theory.
• The anomalous dimensions of renormalized operators can be determined from these computations.
• This work validates the hexagon formalism in a specific sector.