Kinematics, cluster algebras and Feynman integrals

Understand

We identify cluster algebras for planar kinematics of conformal Feynman integrals in four dimensions, as sub-algebras of that for top-dimensional $G(4,n)$ corresponding to $n$-point massless kinematics.

• We provide evidence that they encode information about singularities of such Feynman integrals, including all-loop ladders with symbol letters given by cluster variables and algebraic generalizations.
• As a highly-nontrivial example, we apply $D_3$ cluster algebra to a $n=8$ three-loop wheel integral, which contains a new square root.
• Based on the $D_3$ alphabet and three new algebraic letters essentially dictated by the cluster algebra, we bootstrap its symbol, which is strongly constrained by the cluster adjacency.