Two Approaches For a Perturbative Expansion in Blobbed Topological Recursion

Abstract

In this paper we continue the perturbative analysis of the quartic Kontsevich model. We investigate meromorphic functions Ω (0) m with m = 1, 2, that obey blobbed topological recursion, by calculating their ribbon graph expansions with a Mathematica program using two complementary methods. In doing so, we determine all vacuum ribbon graphs that contribute to the free energy with genus g = 0 up to fourth order. This is a first step towards complete automation of the calculation of graph expansions in the planar sector.

From scalar fields on quantum spaces to blobbed topological recursion

“…In contrast to the previously considered open graphs, closed graphs have a non-trivial automorphism group. We refer to [Lin22] for a more details about the two methods to produce the perturbative expansion of Ω (g) . Let us focus on the planar sector to illustrate the structures.…”

“…, providing again evidence for the correctness of the creation operator. In [Lin22] the full list of graphs contributing to F 0) up to order λ 4 is given, together with the order of their automorphism groups.…”