English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We initiate an exploration of on-shell functions in $\mathcal{N}=4$ SYMbeyond the planar limit by providing compact, combinatorial expressions for allleading singularities of MHV amplitudes and showing that they can always beexpressed as a positive sum of differently ordered Parke-Taylor treeamplitudes. 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-shelldiagram can be associated with many different "positive" regions, of which thefamiliar positive region associated with planar diagrams is just one example.The decomposition into Parke-Taylor factors is simply a "triangulation" ofthese extended positive regions. The $U(1)$ decoupling and Kleiss-Kuijf (KK)relations satisfied by the Parke-Taylor amplitudes also follow naturally fromthis geometric picture. These results suggest that non-planar MHV amplitudes in$\mathcal{N}=4$ SYM at all loop orders can be expressed as a sum ofpolylogarithms weighted by color factors and (unordered) Parke-Tayloramplitudes.

On-Shell Structures of MHV Amplitudes Beyond the Planar Limit