Algebraic Combinatorics Seminar - Ali Mahmoud

Title: 2-Connected Chord Diagrams and Applications in QFT

Abstract:

A functional equation for 2-connected chord diagrams is derived, then is used to calculate asymptotic information for the number of 2-connected chord diagrams by means of alien derivatives applied to factorially divergent power series. The calculation extends the older result by D. J. Kleitman on counting irreducible diagrams. Namely, Kleitman’s result calculates the first coefficient of the infinite asymptotic expansion derived here and is therefore a linear approximation of the result presented here. In calculating the asymptotics this way we are following the approach M. Borinsky used for solving the asymptotic counting problem of general connected chord diagrams. The numbers of 2-connected chord diagrams and the sequence of coefficients of their asymptotic expansion amazingly also appeared, without being recognized, in physics contexts in the work of Broadhurst on 4-loop Dyson-Schwinger-Johnson anatomy, and among the renormalized quantities of quenched QED calculated by M. Borinsky. The underlying chord-diagrammatic structure of quenched QED and Yukawa theory is unveiled here.