Supersymmetric Tools in Yang-Mills Theories at Strong Coupling: the Beginning of a Long Journey

Abstract

Development of holomorphy-based methods in super-Yang-Mills theories started in the early 1980s and lead to a number of breakthrough results. I review some results in which I participated. The discovery of Seiberg's duality and the Seiberg-Witten solution of $\mathcal{N}=2$ Yang-Mills were the milestones in the long journey of which, I assume, much will be said in other talks. I will focus on the discovery (2003) of non-Abelian vortex strings with various degree of supersymmetry, supported in some four-dimensional Yang-Mills theories and some intriguing implications of this discovery. One of the recent results is the observation of a soliton string in the bulk $\mathcal{N}=2$ theory with the $U(2)$ gauge group and four flavors, which can become critical in a certain limit. This is the case of a "reverse holography," with a very transparent physical meaning.

Based on the talk at the Dirac Medal Award Ceremony, ICTP, March 22, 2017. 25 pp, 8 figures; V.2: three references and a brief comment are added

References in corpus (6)

• Theta, Time Reversal, and Temperature
• Gauge/Gravity Duality and Warped Resolved Conifold
• Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2 Supersymmetric QCD
• The Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation
• Critical Non-Abelian Vortex in Four Dimensions and Little String Theory
• N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions

Cited by in corpus (6)

• Anomaly matching in QCD thermal phase transition
• 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
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• Some comments about emission channels of non abelian vortices
• $\beta$-function of the level-zero Gross-Neveu model