113 research outputs found
Scattering amplitude annihilators
Several second order differential operators are shown to annihilate the YM
and GR tree scattering amplitudes. In particular we prove a conjecture of
Loebbert, Mojaza and Plefka from their investigation of a hidden conformal
symmetry in GR.Comment: 31 pages; v2: edits in various sections to improve clarity; computer
code included in an appendix; v3: acknowledgments adde
Scattering amplitudes in YM and GR as minimal model brackets and their recursive characterization
Attached to both Yang-Mills and General Relativity about Minkowski spacetime
are distinguished gauge independent objects known as the on-shell tree
scattering amplitudes. We reinterpret and rigorously construct them as
minimal model brackets. This is based on formulating YM and GR as
differential graded Lie algebras. Their minimal model brackets are then given
by a sum of trivalent (cubic) Feynman tree graphs. The amplitudes are gauge
independent when all internal lines are off-shell, not merely up to
isomorphism, and we include a homological algebra proof of this fact. Using the
homological perturbation lemma, we construct homotopies (propagators) that are
optimal in bringing out the factorization of the residues of the amplitudes.
Using a variant of Hartogs extension for singular varieties, we give a rigorous
account of a recursive characterization of the amplitudes via their residues
independent of their original definition in terms of Feynman graphs (this does
neither involve so-called BCFW shifts nor conditions at infinity under such
shifts). Roughly, the amplitude with legs is the unique section of a sheaf
on a variety of complex momenta whose residues along a finite list of
irreducible codimension one subvarieties (prime divisors) factor into
amplitudes with less than legs. The sheaf is a direct sum of rank one
sheaves labeled by helicity signs. To emphasize that amplitudes are robust
objects, we give a succinct list of properties that suffice for a dgLa so as to
produce the YM and GR amplitudes respectively.Comment: 51 page
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