Quivers for coloured planar $\phi^n$ theories at all loop orders for scattering processes from Feynman diagrams

TL;DR

This paper develops a systematic method to construct quivers for coloured planar $\,\phi^n$ theories at all loop orders, enabling better understanding of scattering processes from Feynman diagrams.

Contribution

It introduces Feynman-like rules for quiver construction applicable to any loop order and extends to mixed and $\,\phi^n$ theories, advancing the computational framework.

Findings

Successfully constructs quivers for two-loop and higher for coloured planar $\,\phi^3$ theory.

Extends quiver construction to general $\,\phi^n$ theories and mixed theories.

Provides a unified approach for all loop orders in these theories.

Abstract

We introduce Feynman-like rules to compute quivers for two loops and higher for the coloured planar $\phi^3$ theory for winding number zero. We demonstrate this for a few cases. Then we extend this further to the case of $\phi^n$ theories, for any n. We also construct the quivers for mixed theories. We do this at all loop order.