So far we have collected the following facts: strictly nested oneloop graphs produce antipodes with rational coefficients in a minimal subtraction scheme. These rational numbers are associated with the fact that no knots appeared in the skein tree of the link diagram attributed to such graphs. Further, crossed ladder topologies provide ζ(2l – 3), associated with the (2, 2l – 3) torus knots, attributed to the crossed ladder topology. Crossed ladder topologies as considered in Chapter 7 are free of subdivergences.

Thus, we have not yet considered the case of subdivergences other than nested. This case is considered in this chapter. We remain in the class of iterated one-loop graphs, but consider other configurations than those covered in Chapter 4 and so extend the analysis to more general rooted trees or bracket configurations.

In this chapter we consider Feynman graphs which are calculable in terms of one-loop letters Г[1], ∑[1] and Ω[1]. The letters are realized by one-loop words in Yukawa theory and are defined below.

While in Chapter 7 we considered primitive Feynman diagrams and increased the loop order, such that d(w) = l(w) = 1, n(w) ≥ 3, now we demand n(w) = l(w), 1 < d(w) < l(w). The condition n(w) = l(w) guarantees that all iPWs w consist of one-loop letters. The resulting iPWs are called one-loop words. The condition 1 < d(w) < l(w) gurantees that we have nested and disjoint subdivergences present at the same time.