Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops

Details Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops

1996-09-16

arxiv.org/abs/hep-th/9609128v3

Phys.Lett. B393 (1997) 403-412

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, Latex, figures using EPSF, replaced version has references and conclusions updated, Eq.(7) revised; as to appear in

Scientific paper

10.1016/S0370-2693(96)01623-1

It is found that the number, $M_n$, of irreducible multiple zeta values (MZVs) of weight $n$, is generated by $1-x^2-x^3=\prod_n (1-x^n)^{M_n}$. For $9\ge n\ge3$, $M_n$ enumerates positive knots with $n$ crossings. Positive knots to which field theory assigns knot-numbers that are not MZVs first appear at 10 crossings. We identify all the positive knots, up to 15 crossings, that are in correspondence with irreducible MZVs, by virtue of the connection between knots and numbers realized by Feynman diagrams with up to 9 loops.

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