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

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.

Based on the talk at the Centennial Meeting of The American Physical Society, March 20-26, Atlanta, GA. LaTex (uses sprocl.sty), 36 pages, 5 eps figures included

Cited by in corpus (14)

• New Instanton Effects In Supersymmetric QCD
• On exact superpotentials in confining vacua
• The beta function of N=1 SYM in Differential Renormalization
• Two-loop renormalization of the Faddeev--Popov ghosts in $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• Three-loop contribution of the Faddeev-Popov ghosts to the $\beta$-function of $\mathcal{N}=1$ supersymmetric gauge theories and the NSVZ relation
• The gaugino condensate from asymmetric four-torus with twists
• Instantons at Strong Coupling, Averaging over Vacua, and the Gluino Condensate
• N=1 Super Yang Mills renormalization schemes for Fractional Branes
• Supersymmetric Tools in Yang-Mills Theories at Strong Coupling: the Beginning of a Long Journey
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• Green Functions of N=1 SYM and Radial/Energy-Scale Relation
• Exact beta function from the holographic loop equation of large-N QCD_4
• Wilson loops in the adjoint representation and multiple vacua in two-dimensional Yang-Mills theory
• Twisted local systems solve the (holographic) loop equation of large-N QCD_4