Spin chain integrability in non-supersymmetric Wilson loops

TL;DR

This paper investigates the integrability of the 1-loop dilatation operator in a generalized Wilson loop in ${\cal N}=4$ super Yang-Mills, demonstrating integrability at specific endpoints and for certain insertions.

Contribution

It shows that the 1-loop dilatation operator remains integrable in a generalized Wilson loop at both endpoints of the interpolation and for specific operator insertions.

Findings

Integrability holds for $SO(6)$ scalar insertions at the endpoints.

Integrability persists for $SU(2|3)$ insertions in the ordinary Wilson loop.

Dynamical spin chain length does not break integrability in these cases.

Abstract

We study the 1-loop dilatation operator for insertions of composite operators in a generalized Wilson loop in ${\cal N}=4$ super Yang-Mills, which interpolates between the supersymmetric Wilson-Maldacena loop and the ordinary Wilson loop with no scalar coupling. For $SO(6)$ scalar insertions, we show that the 1-loop dilatation operator is integrable for the endpoints of the interpolation, i.e. either for the Wilson-Maldacena or the ordinary Wilson loop. Moreover, we also show that integrability persists for $SU(2|3)$ insertions in the ordinary Wilson loop, even when the term making the spin chain length dynamical is included.