1. Geometry from Integrability: Multi-Leg Fishnet Integrals in Two Dimensions
- Author
-
Duhr, Claude, Klemm, Albrecht, Loebbert, Florian, Nega, Christoph, and Porkert, Franziska
- Subjects
High Energy Physics - Theory - Abstract
We generalise the geometric analysis of square fishnet integrals in two dimensions to the case of hexagonal fishnets with three-point vertices. Our results support the conjecture that fishnet Feynman integrals in two dimensions, together with their associated geometry, are completely fixed by their Yangian and permutation symmetries. As a new feature for the hexagonal fishnets, the star-triangle identity introduces an ambiguity in the graph representation of a given Feynman integral. This translates into a map between different geometric interpretations attached to a graph. We demonstrate explicitly how these fishnet integrals can be understood as Calabi-Yau varieties, whose Picard-Fuchs ideals are generated by the Yangian over the conformal algebra. In analogy to elliptic curves, which represent the simplest examples of fishnet integrals with four-point vertices, we find that the simplest examples of three-point fishnets correspond to Picard curves with natural generalisations at higher loop orders., Comment: 51 pages, v2: section 3.5 improved, typos corrected
- Published
- 2024