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.
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