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 β-function of O(N) ϕ4 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.
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Acknowledgements
It is with pleasure that I thank the organizers of the meeting for permission to include this article in these proceedings. It is based on a talk presented at Quantum Field Theory, Periods and Polylogarithms III, Humboldt University, Berlin in June 2012 which was also in honour of Dr D.J. Broadhurst’s 65th birthday. The Axodraw package, [24], was used to draw the figures in the article.
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Gracey, J.A. (2013). Conformal Methods for Massless Feynman Integrals and Large N f Methods. In: Schneider, C., Blümlein, J. (eds) Computer Algebra in Quantum Field Theory. Texts & Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1616-6_4
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