Exponential suppression with four legs and an infinity of loops

TL;DR

This paper solves the Dyson-Schwinger equation for ladder diagrams in massless phi^3 theory, revealing an exponential suppression at strong coupling, and provides explicit expressions involving polylogarithms.

Contribution

It presents an exact solution for the sum of ladder diagrams in phi^3 theory and demonstrates exponential decay at strong coupling.

Findings

Sum of ladder diagrams vanishes exponentially at strong coupling

Explicit polylogarithmic expressions for ladder diagrams

Finite off-shell 4-point functions in massless phi^3 theory

Abstract

The L-loop 4-point ladder diagram of massless phi^3 theory is finite when all 4 legs are off-shell and is given in terms of polylogarithms with orders ranging from L to 2L. We obtain the exact solution of the linear Dyson-Schwinger equation that sums these ladder diagrams and show that this sum vanishes exponentially fast at strong coupling.