Into the wedge of $\mathcal{N}=2$ superconformal gauge theories

TL;DR

This paper explores a new class of Wilson loops in 4D $ ext{SU}(N)$ $ ext{N}=2$ super-Yang-Mills theories, proposing a matrix model description, confirming it with three-loop calculations, and analyzing large-$N$ behavior revealing a phase transition.

Contribution

It introduces a novel matrix model for $rac{1}{4}$-BPS Wilson loops in $ ext{N}=2$ theories and verifies its predictions with explicit perturbative calculations.

Findings

Matrix model accurately predicts Wilson loop values.

Explicit three-loop calculations confirm the matrix model.

Large-$N$ limit shows a phase transition at a critical opening angle.

Abstract

We study $\frac{1}{4}$-BPS Wilson loops in four-dimensional SU$(N$) ${\mathcal{N}}=2$ super-Yang-Mills theories with conformal matter in an arbitrary representation $\mathcal{R}$. These operators are formed of two meridians on the two-sphere separated by an arbitrary opening angle. We conjecture that these observables are encoded in a modification of Pestun's matrix model. The matrix representation of these operators resembles that of the $\frac12$-BPS circular Wilson loop, differing only for a rescaling in the exponent. We compare the matrix model predictions with an explicit three-loop calculation in flat space based on standard Feynman-diagram techniques, finding perfect agreement. Finally, exploiting the matrix model representation of these Wilson loops, we study the large-$N$ limit at strong coupling of $\mathcal{N}=2$ superconformal QCD, finding a surprising transition in the vacuum expectation value for a critical opening angle.