Supersymmetric Gauge Theories and their Dualities

In this course, I will review supersymmetric gauge theories in 4 and 3 spacetime dimensions. I will discuss (Seiberg-like) dualities among these gauge theories, focusing on the example of supersymmetric QCD specific to 4 and 3 dimensions. Towards the end of the course, I will touch upon the non-trivial problem of reducing 4D dualities to 3D dualities, as well as brane-realizations of the gauge theories in question.

• Introduction/Motivation
• 4D
  • Supersymmetric gauge theories in 4D: N=1, N=2, N=4
  • Electric/magnetic duality
  • SQCD (matter content, global symmetries, moduli space, phase structure, RG analysis)
  • Seiberg duality
• 3D
  • SQCD in 3D
  • 3D dualities
• Reduction from 4D to 3D
• Brane picture

• J.Polchinski, Dualities of Fields and Strings, arXiv:1412.5704
• M. Dine, Ch. 9 from Supersymmetry and String Theory, Cambridge University Press
• M. Bertolini, Ch. 6 from Lectures on Supersymmetry
• N. Seiberg, Electric - magnetic duality in supersymmetric non-Abelian gauge theories , hep-th/9411149
• K. Intriligator, N. Seiberg, Lectures on supersymmetric gauge theories and electric-magnetic duality , hep-th/9509066
• O. Aharony, IR duality in d = 3 N=2 supersymmetric USp(2N(c)) and U(N(c)) gauge theories., hep-th/9703215
• O. Aharony, S. S. Razamat, N. Seiberg, and B. Willett. 3d dualities from 4d dualities. arXiv: 1305.3924 [hep-th].

The material of this course is more or less contained in my review article String theory and the 4D/3D reduction of Seiberg duality. A Review. However in the review, there is less emphasis on the introductory material and a lot more advanced material, in particular many generalizations of the dualities discussed in the course.