Probing N=2 superconformal field theories with localization

TL;DR

This paper uses supersymmetric localization to analyze N=2 superconformal field theories, deriving eigenvalue densities, exploring holographic dual conditions, and computing Wilson loop observables and related quantities.

Contribution

It introduces a unique eigenvalue density equation for N=2 SCFTs and connects eigenvalue distributions to holographic dual conditions, with explicit calculations of Wilson loop observables.

Findings

Eigenvalue density matches Wigner distribution under certain conditions.

Wilson loop expectation values differ significantly from N=4 SYM when fundamental matter is present.

Holographic duality conditions relate to eigenvalue density properties.

Abstract

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