Science ParkComenius University in Bratislava

Seminar of Theoretical Physics - Anton Zajac (15.11.2019)

Friday 15.11.2019 at 15:00 hod., Lecture room F2/125

10. 11. 2019 21.53 hod.
By: Peter Maták

Anton Zajac (Imperial College London):
First Lecture in Supersymmetric Quiver Gauge Theories: The Vacuum Moduli Space of SQED


The vacuum moduli space of supersymmetric gauge theories is one of the widest windows through which one can glance at the inner workings of the Nature (should it turn out supersymmetric\footnote{Lets hope it does!}). We consider the simplest supersymmetric quiver gauge theory in $4$ dimensions -- the SQED. First, the structure of the Lagrangian for SQED is derived, starting from QED and the supersymmetry invariance. Once the susy invariant Lagrangian is obtained the computation of the moduli space of vacua (in particular the Higgs branch) is straightforward to preform. It is a classical computation which involves finding the minimum of the susy potential. We show that the Higgs branch of SQED (the Coulomb branch is identically the same in this case) is a nilpotent orbit of $\mathfrak{su}(2)$ algebra. The equivalence of the Higgs and the Coulomb branch of the moduli space of SQED (both maximal nilpotent orbits of $\mathfrak{su}(2)$) provides the first-hand example of 3d self-mirror symmetry.