$\mathcal{N}=4$ single-minus superamplitudes and dual superconformal symmetry

We construct the $\mathcal{N}=4$ supersymmetric completion of the recently proposed single-minus gluon amplitudes in $(2,2)$ signature, which are nonvanishing for all multiplicities on a half-collinear kinematic locus. The superamplitude factorises into a permutation-invariant measure $\Delta^{(n-1)}$ with uniform little-group weight that imposes the half-collinearity constraint, a piecewise constant stripped amplitude $\tilde{A}_{1\ldots n}$ that is helicity blind and dual conformal invariant, and (super)momentum conservation delta functions. For $n=3$, our superamplitude reduces to the known $\overline{\rm MHV}$ superamplitude. We prove dual superconformal covariance of the $n$-point superamplitude, and further analyse the $\mathrm{Gr}(k,n)$ Grassmannian integral at $k=1$. Finally, we present the corresponding single-minus superamplitude in $\mathcal{N}=8$ supergravity.