All-plus Yang--Mills and gravity wavefunctions in de Sitter space

Abstract

We present sewing representations for tree-level all-plus wavefunctions in four-dimensional de Sitter space. For Yang--Mills theory, the arbitrary-multiplicity formula is a sum over noncrossing polygon dissections, with each cell carrying energy differences of a full lower-point wavefunction. The absence of a generic total-energy pole is manifest, while partial-energy residues are determined by the lower-point factors. We derive this representation from self-dual Yang--Mills solutions. For Einstein gravity, we propose an arbitrary-multiplicity formula consisting of an alternating sum over labelled sewing trees plus a local gravitational Chern--Simons term. This local term arises from the self-dual Einstein action and supplies boundary data not fixed by internal-energy cuts. We derive a generating formula for it from the boundary connection and give explicit expressions through seven points.