  We consider correlation functions of supersymmetrized determinant operators
in self-dual super Yang-Mills (SYM). These provide a generating function for
correlators of arbitrary single-trace half-BPS operators, including, for
appropriate Grassmann components, the so-called loop integrand of the
non-self-dual theory. We introduce a novel twistor space representation for
determinant operators which makes contact with the recently studied $m=2$
amplituhedron. By using matrix duality we rewrite the $n$-point determinant
correlator as a $n\times n$ matrix integral where the gauge group rank $N_c$ is
turned into a coupling. The correlators are rational functions whose
denominators, in the planar limit, contain only ten-dimensional distances.
Using this formulation, we verify a recent conjecture regarding the
ten-dimensional symmetry of the components with maximal Grassmann degree and we
obtain new formulas for correlators of Grassmann degree four.
