BPS wilson loops in generic conformal $$ \mathcal{N} $$ = 2 SU(N) SYM theories

Abstract

A bstract We consider the 1/2 BPS circular Wilson loop in a generic $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 SU( N ) SYM theory with conformal matter content. We study its vacuum expectation value, both at finite N and in the large- N limit, using the interacting matrix model provided by localization results. We single out some families of theories for which the Wilson loop vacuum expectation values approaches the $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 result in the large- N limit, in agreement with the fact that they possess a simple holographic dual. At finite N and in the generic case, we explicitly compare the matrix model result with the field-theory perturbative expansion up to order g 8 for the terms proportional to the Riemann value ζ (5), finding perfect agreement. Organizing the Feynman diagrams as suggested by the structure of the matrix model turns out to be very convenient for this computation.