Determinants in self-dual N=4 SYM and twistor space

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 x 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.

Automated summary

This article investigates correlation functions of supersymmetrized determinant operators in self-dual super Yang-Mills theory. These correlation functions generate correlators of arbitrary single-trace half-BPS operators, including the loop integrand of the non-self-dual theory for appropriate Grassmann components. A novel twistor space representation for determinant operators is introduced, which connects with the recently studied m = 2 amplituhedron. By using matrix duality, the n-point determinant correlator is rewritten as an n x n matrix integral with the gauge group rank N-c becoming a coupling constant. The correlators are rational functions with denominators containing only ten-dimensional distances in the planar limit. Using this formulation, a recent conjecture regarding the ten-dimensional symmetry of the components with maximal Grassmann degree is verified, and new formulas for correlators of Grassmann degree four are obtained.