Conformal methods for massless Feynman integrals and large N_f methods

TL;DR

This paper reviews conformal integration techniques and large N methods for calculating renormalization group functions in quantum field theories, exemplified by O(N) phi^4 theory, and discusses future research directions.

Contribution

It introduces a conformal integration approach combined with large N methods to compute high-order renormalization group functions, including an explicit O(1/N^2) calculation.

Findings

Applied conformal methods to a beta-function graph in O(N) phi^4 theory

Demonstrated the calculation of high-order terms using large N techniques

Discussed potential future developments in large N methods

Abstract

We review the large N method of calculating high order information on the renormalization group functions in a quantum field theory which is based on conformal integration methods. As an example these techniques are applied to a typical graph contributing to the beta-function of O(N) phi^4 theory at O(1/N^2). The possible future directions for the large N methods are discussed in light of the development of more recent techniques such as the Laporta algorithm.