Tracy-Widom Distribution in Four-Dimensional Supersymmetric Yang-Mills Theories

Area of Science:

• High-energy theoretical physics
• Quantum field theory
• Supersymmetry

Background:

• Four-dimensional superconformal Yang-Mills theories possess complex dynamics.
• Exact computation of observables is crucial for understanding these theories.
• Fredholm determinants of truncated Bessel operators offer a pathway to exact solutions.

Purpose of the Study:

• To determine the dependence of various observables on the 't Hooft coupling constant.
• To develop a method for strong coupling expansions.
• To investigate the inclusion of nonperturbative corrections and resurgent properties.

Main Methods:

• Utilizing Fredholm determinants of truncated Bessel operators for exact observable computations.
• Analyzing the behavior of weak and strong coupling expansions.
• Developing a systematic method to compute nonperturbative, exponentially small corrections.

Main Results:

• Established an exact method for computing observables in specific superconformal Yang-Mills theories.
• Demonstrated that strong coupling expansions are factorially divergent.
• Developed a technique to systematically incorporate nonperturbative corrections into transseries expansions.

Conclusions:

• The strong coupling regime requires nonperturbative corrections for a complete description.
• The developed method provides a systematic approach to analyze these corrections.
• The resurgent properties of the transseries offer deeper insights into the theory's behavior.