Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory

Area of Science:

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

Background:

• Planar N=4 supersymmetric Yang-Mills theory is a key model in high-energy physics.
• Correlation functions are essential for understanding quantum field theory dynamics.
• Gauge-string duality provides a powerful bridge between quantum field theories and string theory.

Purpose of the Study:

• To introduce a nonperturbative approach for calculating correlation functions involving determinant and single-trace operators.
• To leverage gauge-string duality to propose a novel interpretation of these correlation functions.
• To provide testable predictions for correlation functions at finite coupling.

Main Methods:

• Utilizing a nonperturbative approach to analyze correlation functions.
• Applying gauge-string duality to map quantum field theory operators to string theory states.
• Determining integrable boundary states using symmetry and integrability of the dual superstring sigma model.

Main Results:

• Proposed that correlation functions correspond to overlaps on the string world sheet.
• Derived expressions for correlators at finite coupling.
• Conjectured the validity of these expressions for operators of arbitrary size.

Conclusions:

• The study presents a novel framework for understanding correlation functions in planar N=4 supersymmetric Yang-Mills theory.
• The proposed method, grounded in gauge-string duality, offers a new perspective on the relationship between quantum field theory and string theory.
• The derived expressions and conjectures provide a foundation for future investigations and experimental verification.