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

A bstract We study $$ \frac{1}{4} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>4</mml:mn> </mml:mfrac> </mml:math> -BPS Wilson loops in four-dimensional SU( N ) $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 super-Yang-Mills theories with conformal matter in an arbitrary representation $$ \mathcal{R} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> </mml:math> . 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 $$ \frac{1}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> -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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 superconformal QCD, finding a surprising transition in the vacuum expectation value for a critical opening angle.