On non-supersymmetric generalizations of the Wilson-Maldacena loops in N=4 SYM

Abstract

Building on our previous work arXiv:1712.06874 we consider one-parameter Polchinski-Sully generalization of the Wilson-Maldacena (WM) loops in planar N=4 SYM theory. This breaks local supersymmetry of WM loop and leads to running of the deformation parameter $ζ$. We compute the three-loop ladder diagram contribution to the expectation value of the circular loop which gives the full answer for large $ζ$. The limit $ζ\gg 1$, $λζ^2=$ fixed in which the expectation value is determined by the Gaussian adjoint scalar path integral might be exactly solvable despite the lack of global supersymmetry. We study similar generalization of the 1/4-BPS "latitude" WM loop which depends on two parameters (in addition to the 't Hooft coupling $λ$). One may also introduce another supersymmetry-breaking parameter -- the winding number of the scalar coupling circle. We find the two-loop expression for the expectation value of the associated loop by combining the ladder diagram contribution with an indirect determination of the non-ladder contribution using 1d defect CFT perturbation theory.