# Is there a relation between various vertices in Yang-Mills theory?

In Yang-Mills theories (and more complicated theories with additional matter fields) we have three and four gauge boson vertices, boson-ghost and boson-matter vertices. Perturbative divergences present in all of them are perfectly correlated - once divergences in propagators are removed by rescaling of fields and massess, we can absorb all divergences in vertices by a redefinition of single coupling constant. This makes me wonder whether some relations hold also between finite parts of vertices.

Two remarks

1. I am aware of the spinor-helicity machinery. As far as I understand this applies mostly to scattering amplitudes of on-shell gluons. My question is about something more general, namely arbitrary correlation functions $\langle A(x_1)...A(x_n) \rangle$ in some gauge.
2. I know about Slavnov-Taylor identities, BRST invariance and all that. However I have no idea how to use this machinery to look for relations between $\langle AAA \rangle$ and $\langle AAAA \rangle$ or $\langle \bar c c A \rangle$. I have some partial results involving these three vertices, but unfortunately it involves also higher vertices $\langle \bar c c A A \rangle$.
• Do you mean the vertices from the Feynman rules, or correlation functions (which are the sums of all amputated diagrams)? – Prof. Legolasov Feb 8 '18 at 5:52
• I am mostly interested in proper vertices, which are sums of 1PI diagrams. Statement about other correlation functions (e.g. all connected) would be equally interesting. – Blazej Feb 8 '18 at 19:47
• Afaik Slavnov-Taylor is exactly what you are looking for. Not sure what you mean by “don’t know how to derive relations”, Slavnov-Taylor are the relations. Or do you mean algebraic relations (not involving space time derivatives)? In this case I don’t think there is anything like it out there. – Prof. Legolasov Feb 9 '18 at 2:30