Complexes of marked graphs in gauge theory

© 2020, The Author(s). 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 with graphs. Furthermore, we describe a universal model for these kinds of complexes which allows to treat all of them in a unified way.