# Complexes of marked graphs in gauge theory

## TL;DR

This paper reviews and computes the cohomology of gauge and ghost cycle graph complexes, revealing a unified framework for these graph-based algebraic structures in gauge theory.

## Contribution

It introduces a universal model for gauge and ghost cycle graph complexes, enabling a unified treatment and deeper understanding of their algebraic properties.

## Key findings

- Computed the cohomology of gauge and ghost cycle graph complexes.
- Unified various complexes under a general double complex framework.
- Provided a universal model for analyzing graph-based complexes in gauge theory.

## Abstract

We review the gauge and ghost cyle graph complexes as defined by Kreimer, Sars and van Suijlekom in "Quantization of gauge fields, graph polynomials and graph homology" and compute their cohomology. These complexes are generated by labelings on the edges or cycles of graphs and the differentials act by exchanging these labels. We show that both cases are instances of a more general construction of double complexes associated to graphs. Furthermore, we describe a universal model for these kind of complexes which allows to treat all of them in a unified way.