Cutting Multiparticle Correlators Down to Size

Understand

Multiparticle correlators are mathematical objects frequently encountered in quantum field theory and collider physics.

• By translating multiparticle correlators into the language of graph theory, we can gain new insights into their structure as well as identify efficient ways to manipulate them.
• In this paper, we highlight the power of this graph-theoretic approach by "cutting open" the vertices and edges of the graphs, allowing us to systematically classify linear relations among multiparticle correlators and develop faster methods for their computation.
• The naive computational complexity of an $N$-point correlator among $M$ particles is $\mathcal O(M^N)$, but when the pairwise distances between particles can be cast as an inner product, we show that all such correlators can be computed in linear $\mathcal O(M)$ runtime.