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−1MHV helicity structure, dressed by ordinary Minkowski amplitudes. We derive all the N−1MHV 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.
Highlights
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
We find that static-patch scattering for Yang-Mills is subject to BCFW-like recursion relations
Summary
It is crucial to set up the calculation in a way that makes best use of available symmetries. In [9], we proposed a general strategy for the static-patch problem, which makes use of the larger symmetry of dS4 as a whole This involves artificially extending the static patch’s boundaries into geodesically complete cosmological horizons, each one defining a Poincare patch. For Yang-Mills theory, the static-patch scattering problem, while less trivial than the Minkowski S-matrix, is easier than standard (A)dS boundary correlators, despite having nominally lower symmetry. The results for these amplitudes are given in eqs. These are given in eqs. (5.2)–(5.3). section 6 is devoted to discussion and outlook
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