Gluing Ladder Feynman Diagrams into Fishnets.

Area of Science:

• Quantum Field Theory
• Mathematical Physics

Background:

• Integrability is a powerful tool for solving quantum field theories.
• Fishnet diagrams are a specific class of Feynman diagrams relevant in certain quantum field theories.

Purpose of the Study:

• To compute four-point correlation functions in planar phi^4 theory using fishnet diagrams.
• To explore the structure of these diagrams and identify underlying mathematical relationships.

Main Methods:

• Utilizing integrability at weak coupling to calculate fishnet diagrams.
• Analyzing the resulting multilinear combinations of ladder integrals.
• Applying Steinmann relations as a constraint.

Main Results:

• The computation yielded results as multilinear combinations of ladder integrals.
• Ladder integrals were found to be constructed from classical polylogarithms.
• A conjecture was proposed: any fishnet diagram can be represented as the determinant of a matrix of ladder integrals.

Conclusions:

• The study successfully computed fishnet diagrams for four-point correlation functions.
• Integrability and Steinmann relations provide strong constraints on the structure of these diagrams.
• The determinant conjecture offers a new perspective on the organization of fishnet diagrams.