MHV amplitudes and BCFW recursion for Yang-Mills theory in the de Sitter static patch
arXiv:2105.07572 · doi:10.1007/JHEP09(2021)176
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.
arXiv comment40 pages, 3 figures; v2: JHEP version; expanded discussion, references; v3: corrected the kinematics of reading off the final horizon data
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