Integrated Correlators in N=4 Supersymmetric Yang-Mills Theory beyond Localization

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.
• Integrated correlators are important observables in this theory.
• Calculating these correlators is challenging, especially for arbitrary charges.

Purpose of the Study:

• To develop a method for calculating integrated correlators of four superconformal primaries.
• To find an exact expression for these correlators in the planar limit.
• To verify the expression against known results.

Main Methods:

• Analyzing integrated correlators of four superconformal primaries O_p.
• Utilizing supersymmetric localization for specific cases.
• Summing contributions from different channels to cancel multiple zeta values.
• Proposing an exact expression for arbitrary 't Hooft coupling.

Main Results:

• A general formula for integrated correlators in the planar limit of N=4 super Yang-Mills theory.
• Cancellation of complex multiple zeta values, leaving only specific zeta functions.
• The formula successfully reproduces known results from localization, perturbation theory, and strong-coupling expansions.
• Application to determine Feynman integral periods and strong-coupling coefficients.

Conclusions:

• The proposed exact expression provides a unified approach to calculating integrated correlators.
• This work simplifies complex calculations and offers new insights into N=4 super Yang-Mills theory.
• The findings have implications for understanding quantum field theories and related areas like string theory.