On-shell structures of MHV amplitudes beyond the planar limit
We initiate an exploration of on-shell functions in N = 4 SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHV amplitudes and showing that they can always be expressed as a positive sum of differently ordered Parke-Taylor tree amplitudes. T...
| Príomhchruthaitheoirí: | , , , , |
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| Rannpháirtithe: | |
| Formáid: | Alt |
| Teanga: | en_US |
| Foilsithe / Cruthaithe: |
Springer-Verlag
2015
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| Rochtain ar líne: | http://hdl.handle.net/1721.1/98234 https://orcid.org/0000-0002-3964-8870 |
| Achoimre: | We initiate an exploration of on-shell functions in N = 4 SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHV amplitudes and showing that they can always be expressed as a positive sum of differently ordered Parke-Taylor tree amplitudes. This is understood in terms of an extended notion of positivity in G(2, n), the Grassmannian of 2-planes in n dimensions: a single on-shell diagram can be associated with many different “positive” regions, of which the familiar G [subscript +](2, n) associated with planar diagrams is just one example. The decomposition into Parke-Taylor factors is simply a “triangulation” of these extended positive regions. The U(1) decoupling and Kleiss-Kuijf (KK) relations satisfied by the Parke-Taylor amplitudes also follow naturally from this geometric picture. These results suggest that non-planar MHV amplitudes in N = 4 SYM at all loop orders can be expressed as a sum of polylogarithms weighted by color factors and (unordered) Parke-Taylor amplitudes. |
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