9 SU(2) theory with 4 flavors and Gaiotto’s duality

In this section we start with the analysis of SU(2) gauge theory with Nf = 4 flavors. We will see that it can naturally generalized to the analysis of a whole zoo of theories with the gauge group of the form SU(2)n. The discussions basically follow the first half of the seminal paper [8].

 9.1 The curve as λ2 = ϕ2(z)
 9.2 Identification of parameters
  9.2.1 Coupling constant
  9.2.2 Mass parameters
 9.3 Weak-coupling limit and trifundamentals
 9.4 Strong-coupling limit
 9.5 Generalization
  9.5.1 Trivalent diagrams
  9.5.2 Example: torus with one puncture
  9.5.3 Example: sphere with five punctures
  9.5.4 Example: a genus-two surface
  9.5.5 The curve and the Hitchin field
 9.6 Theories with less flavors revisited
  9.6.1 Rewriting of the curves
  9.6.2 Generalization