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(Extended) Rigid Supersymmetry

Luca Griguolo - University of Parma, Parma

Domenico Seminara - University of Firenze, Firenze

Stefano Cremonesi - King's College, London

  The aim of the course is to introduce the exact solution of the low energy effective action on the Coulomb branch of vacua of N=2 supersymmetric gauge theories in four dimensions, following the seminal work of Seiberg and Witten in 1994. The course is structured in 4 parts:
    1. Monopoles, dyons and electric-magnetic duality.
    2. Basics of N=2 supersymmetry.
    3. The Seiberg-Witten solution of the infrared dynamics of N=2 SU(2) SYM.
    4. Generalizations and the M-theory realization of the SW curve.
  Parts 1 and 2 are introductory. I will only assume standard knowledge of N=1 supersymmetry in 4 dimensions and build from the ground up towards Part 3, which is the core of the course. If time allows I will describe more advanced material (though still quite old) in the final part. At the end of the course you should be able to read about more recent advances such as Argyres-Seiberg and Gaiotto dualities.
  Some original papers:
    Seiberg and Witten, hep-th/9407087 (part 3).
    Witten, hep-th/9703166 (part 4).
  Useful reviews:
    L. Alvarez-Gaumè and S.F. Hassan, Introduction to S duality in N=2 supersymmetric gauge theories: A Pedagogical review of the work of Seiberg and Witten, ArXiv:hep-th/9701069.
    A. Bilal, Duality in N=2 SUSY SU(2) Yang-Mills theory: A Pedagogical introduction to the work of Seiberg and Witten , ArXiv:hep-th/9601007.
    A. Bilal, Introduction to supersymmetry, ArXiv:hep-th/0101055.
    W. Lerche, Introduction to Seiberg-Witten theory and its stringy origin, ArXiv:hep-th/9611190.
    P.C. Argyres, Lectures on Supersymmetry
    J.M. Figueroa O'Farrill, Electromagnetic Duality for Children
    P. Di Vecchia, Duality in N=2, N=4 supersymmetric gauge theories, ArXiv:hep-th/9803026
    Y. Tachikawa, N=2 supersymmetric dynamics for pedestrians, ArXiv:1312.2684 (including recent material which I will not be able to cover)