Spin chain integrability in non-supersymmetric Wilson loops

Abstract

We study the 1-loop dilatation operator for insertions of composite operators in a generalized Wilson loop in 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.