QCD gluon vertices from the string-inspired formalism

The Bern-Kosower formalism, developed around 1990 as a novel way of obtaining QCD amplitudes as the limit of infinite string tension of the corresponding string amplitudes, was originally designed as an on-shell formalism. Building on early work by Strassler, the authors have recently shown that this string-inspired formalism is extremely efficient also as a tool for the study of off-shell amplitudes in QCD, and in particular for achieving compact form factor decompositions of the N-gluon vertices. Among other things, this formalism allows one to achieve a manifestly gauge invariant decomposition of these vertices by way of integration-by-parts, rather than the usual tedious analysis of the non-abelian off-shell Ward identities, and to combine the spin zero, half and one cases. Here, we will provide a summary of the method, as well as its application to the three and four-gluon vertices.