Symbol Alphabets from Tensor Diagrams

Understand

We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of $n$-particle amplitudes in planar $\mathcal{N}=4$ Yang-Mills theory and certain polytopes associated to the Grassmannian G(4, $n$).

• We show how to assign a web (a planar tensor diagram) to each facet of these polytopes.
• Webs with no inner loops are associated to cluster variables (rational symbol letters).
• For webs with a single inner loop we propose and explicitly evaluate an associated web series that contains information about algebraic symbol letters.