An Introduction to Seiberg-Witten Theory, Mapping the Quantum Moduli of N=2 Theories

I will give an introduction to Seiberg-Witten theory, focusing largely on the original pure SU(2) SYM example. In studying the behavior of the theory over the moduli space we will see the emergence of an elliptic fibration (the Seiberg-Witten curve). By leveraging holomorphy and consistency we will be able to fully solve the low energy dynamics of this theory. In particular we will see that at different corners of the moduli space emergent monopoles and dyons become massless operators of an effective U(1) SYM. I will point to features of the approach that generalize to a broader class of N=2 SYM.