Seiberg-Witten Theory and S-Duality

Abstract

In these lectures I am going to give an elementary introduction to the Seiberg-Witten theory, i.e. the exact solutions of N = 2 supersymmetric Yang-Mills theories. Seiberg-Witten solution [1, 2] is the first exact solution in strongly-coupled quantum gauge theories in 4-dimensions. The solution was first constructed for SU(2) Yang-Mills theory with 0 ≤ N f ≤ 4 hypermultiplets in vector representations. It was subsequently generalized to the case of classical gauge groups SU(N), SO(N), Sp(N) [3, 4, 5, 7, 8, 9, 10] and provides a wealth of information on the strong coupling dynamics of gauge theories. There are excellent pedagogical reviews on Seiberg-Witten theory [11, 12, 13].