Calculation of the phi^4 6-loop non-zeta transcendental

Oliver Schnetz

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arXiv · hep-th/9912149

Calculation of the phi^4 6-loop non-zeta transcendental

Oliver Schnetz

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Abstract

We present an analytic calculation of the first transcendental in phi^4-Theory that is not of the form zeta(2n+1). It is encountered at 6 loops and known to be a weight 8 double sum. Here it is obtained by reducing multiple zeta values of depth <= 4. We give a closed expression in terms of a zeta-related sum for a family of diagrams that entails a class of physical graphs. We confirm that this class produces multiple zeta values of weights equal to the crossing numbers of the related knots.

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Oliver Schnetz. 1999-12-16. Calculation of the phi^4 6-loop non-zeta transcendental. https://arxiv.org/abs/hep-th/9912149

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