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

TL;DR

This paper explores non-supersymmetric generalizations of Wilson-Maldacena loops in N=4 SYM, analyzing their expectation values, running parameters, and potential exact solvability despite broken supersymmetry.

Contribution

It introduces a one-parameter deformation of WM loops breaking supersymmetry, computes higher-loop contributions, and studies their behavior in various limits and parameter regimes.

Findings

Three-loop ladder diagram contribution computed.

Large deformation parameter limit may be exactly solvable.

Two-loop expectation value derived using defect CFT techniques.

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 $\zeta$. We compute the three-loop ladder diagram contribution to the expectation value of the circular loop which gives the full answer for large $\zeta$. The limit $\zeta\gg 1$, $\lambda \zeta^2=$ 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 $\lambda$). 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.