MHV amplitudes and BCFW recursion for Yang-Mills theory in the de Sitter static patch

TL;DR

This paper explores scattering in the static patch of de Sitter space, deriving BCFW-like recursion relations for Yang-Mills theory that connect static-patch amplitudes to Minkowski space results.

Contribution

It introduces BCFW-like recursion relations for static-patch Yang-Mills amplitudes, linking them to Minkowski space amplitudes and deriving an infinite set of MHV amplitudes.

Findings

Static-patch scattering for Yang-Mills obeys BCFW-like recursion relations.

All N^{-1}MHV static-patch amplitudes can be derived from self-dual solutions.

An infinite set of MHV amplitudes with arbitrary external legs is obtained.

Abstract

We study the scattering problem in the static patch of de Sitter space, i.e. the problem of field evolution between the past and future horizons of a de Sitter observer. We formulate the problem in terms of off-shell fields in Poincare coordinates. This is especially convenient for conformal theories, where the static patch can be viewed as a flat causal diamond, with one tip at the origin and the other at timelike infinity. As an important example, we consider Yang-Mills theory at tree level. We find that static-patch scattering for Yang-Mills is subject to BCFW-like recursion relations. These can reduce any static-patch amplitude to one with N^{-1}MHV helicity structure, dressed by ordinary Minkowski amplitudes. We derive all the N^{-1}MHV static-patch amplitudes from self-dual Yang-Mills field solutions. Using the recursion relations, we then derive from these an infinite set of MHV amplitudes, with arbitrary number of external legs.