Probing N = 2 $$ \mathcal{N}=2 $$ superconformal field theories with localization

Abstract

We use supersymmetric localization to study probes of four dimensional\nLagrangian N=2 superconformal field theories. We first derive a unique equation\nfor the eigenvalue density of these theories. We observe that these theories\nhave a Wigner eigenvalue density precisely when they satisfy a necessary\ncondition for having a holographic dual with a sensible higher-derivative\nexpansion. We then compute in the saddle-point approximation the vacuum\nexpectation value of 1/2-BPS circular Wilson loops, and the two-point functions\nof these Wilson loops with the Lagrangian density and with the stress-energy\ntensor. This last computation also provides the corresponding Bremsstrahlung\nfunctions and entanglement entropies. As expected, whenever a finite fraction\nof the matter is in the fundamental representation, the results are drastically\ndifferent from those of N=4 supersymmetric Yang-Mills theory.\n