Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory

TL;DR

This paper demonstrates that smooth Maldacena-Wilson loops in N=4 super Yang-Mills theory exhibit a Yangian symmetry, revealing a hidden integrable structure at both weak and strong coupling regimes.

Contribution

It establishes the Yangian invariance of supersymmetrized Wilson loops in N=4 SYM at one-loop and classical string levels, showing a novel symmetry in the theory.

Findings

Yangian symmetry holds at one-loop order in weak coupling.

Yangian symmetry is present at leading order in strong coupling.

Evidence suggests an interpolating function between weak and strong coupling.

Abstract

We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in N=4 super Yang-Mills theory are invariant under a Yangian symmetry Y[psu(2,2|4)] built upon the manifest superconformal symmetry algebra of the theory. The existence of this hidden symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the classical integrability of the dual AdS_5 x S^5 string description. The hidden symmetry generators consist of a canonical non-local second order variational derivative piece acting on the superpath, along with a novel local path dependent contribution. We match the functional form of these Yangian symmetry generators at weak and strong coupling and find evidence for an interpolating function. Our findings represent the smooth counterpart to the Yangian invariance of scattering superamplitudes dual to light-like polygonal super Wilson loops in the N=4 super Yang-Mills theory.