Compatible Cycles and CHY Integrals

Understand

The CHY construction naturally associates a vector in $\mathbb{R}^{(n-3)!}$ to every 2-regular graph with $n$ vertices.

• Partial amplitudes in the biadjoint scalar theory are given by the inner product of vectors associated with a pair of cycles.
• In this work we study the problem of extending the computation to pairs of arbitrary 2-regular graphs.
• This requires the construction of compatible cycles, i.e.