Exact Results in Gauge Theories: Putting Supersymmetry to Work. The 1999 Sakurai Prize Lecture

TL;DR

This paper reviews how supersymmetry enables exact solutions in strong coupling gauge theories, highlighting historical developments, key results like the beta function and gluino condensate, and recent breakthroughs in the field.

Contribution

It summarizes the development and impact of supersymmetry-based methods for obtaining exact results in gauge theories, emphasizing their historical and recent significance.

Findings

Exact calculation of the beta function in supersymmetric gauge theories

Determination of the gluino condensate using supersymmetric methods

Recent breakthroughs leveraging these exact results in gauge theory research

Abstract

Powerful methods based on supersymmetry allow one to find exact solutions to certain problems in strong coupling gauge theories. The inception of some of these methods (holomorphy in the gauge coupling and other chiral parameters, in conjunction with instanton calculations) dates back to the 1980's. I describe the early exact results -- the calculation of the beta function and the gluino condensate -- and their impact on the subsequent developments. A brief discussion of the recent breakthrough discoveries where these results play a role is given.