Posted by In this rather large note we discuss $SU(2)$ Seiberg-Witten theory with one flavour of hypermultiplets. We begin with the UV $\mathcal{N}=2$ actions. A chiral field acquires a vev and the gauge group gets broken to $U(1)$ in the IR. We discuss running of the coupling constant, singularities in the $u$-plane and monodramies around them. Then, we introduce the Seiberg-Witten curve. Finally, we discuss two interesting physical phenomena that appear in the case of one flavour:
- Quark point can be continiously deformed into a monopole point via traversing a closed path in the $\mu$-plane.
- For a special value of the mass parameter $\mu$, one can get a singularity at which both electric and magnetic particles can simultaneously become light. the resulting theory has no Lagrangian description.
To understand this note I recommend consulting the following previous notes whenever necessary: $\mathcal{N}=2$ Supersymmetric Actions, $\mathcal{N}=1$ Supersymmetric Actions, Superspace and Superfields, Electromagnetic Duality.