All non-maximally-helicity-violating one-loop seven-gluon amplitudes in N = 4 super-Yang-Mills theory

We compute the non-MHV (non-maximally-helicity-violating) one-loop seven-gluon amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory, which contain three negative-helicity gluons and four positive-helicity gluons. There are four independent color-ordered amplitudes, $(--\ensuremath{-}++++)$, $(--+\ensuremath{-}+++)$, $(--++\ensuremath{-}++)$ and $(\ensuremath{-}+\ensuremath{-}+\ensuremath{-}++)$. The MHV amplitudes containing two negative-helicity and five positive-helicity gluons were computed previously, so all independent one-loop seven-gluon helicity amplitudes are now known for this theory. We present partial information about an infinite sequence of next-to-MHV one-loop helicity amplitudes, with three negative-helicity and $n\ensuremath{-}3$ positive-helicity gluons, and the color ordering $(--\ensuremath{-}++\ensuremath{\cdots}++)$; we give a new coefficient of one class of integral functions entering this amplitude. We discuss the twistor-space properties of the box-integral-function coefficients in the amplitudes, which are quite simple and suggestive.