Combinatorial Dyson-Schwinger Equations of Quartic Matrix Field Theory

Fuente: arXiv
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Main Authors: Hock, Alexander, Thürigen, Johannes
Format: Preprint
Published: 2024
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author Hock, Alexander
Thürigen, Johannes
author_facet Hock, Alexander
Thürigen, Johannes
contents Matrix field theory is a combinatorially non-local field theory which has recently been found to be a non-trivial but solvable QFT example. To generalize such non-perturbative structures to other models, a more combinatorial understanding of Dyson-Schwinger equations and their solutions is of high interest. To this end we consider combinatorial Dyson-Schwinger equations manifestly relying on the Hopf-algebraic structure of perturbative renormalization. We find that these equations are fully compatible with renormalization, relying only on the superficially divergent diagrams which are planar ribbon graphs, i.e. decompleted dual combinatorial maps. Still, they are of a similar kind as in realistic models of local QFT, featuring in particular an infinite number of primitive diagrams as well as graph-dependent combinatorial factors.
format Preprint
id arxiv_https___arxiv_org_abs_2404_03389
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Combinatorial Dyson-Schwinger Equations of Quartic Matrix Field Theory
Hock, Alexander
Thürigen, Johannes
Mathematical Physics
High Energy Physics - Theory
Matrix field theory is a combinatorially non-local field theory which has recently been found to be a non-trivial but solvable QFT example. To generalize such non-perturbative structures to other models, a more combinatorial understanding of Dyson-Schwinger equations and their solutions is of high interest. To this end we consider combinatorial Dyson-Schwinger equations manifestly relying on the Hopf-algebraic structure of perturbative renormalization. We find that these equations are fully compatible with renormalization, relying only on the superficially divergent diagrams which are planar ribbon graphs, i.e. decompleted dual combinatorial maps. Still, they are of a similar kind as in realistic models of local QFT, featuring in particular an infinite number of primitive diagrams as well as graph-dependent combinatorial factors.
title Combinatorial Dyson-Schwinger Equations of Quartic Matrix Field Theory
topic Mathematical Physics
High Energy Physics - Theory
url https://arxiv.org/abs/2404.03389