# Unitary, anomalous Master Ward Identity and its connections to the Wess-Zumino condition, BV formalism and $L_\infty$-algebras

October 12, 2022

The C*-algebraic construction of QFT by Buchholz and one of us relies on the
causal structure of spacetime and a classical Lagrangian. In one of our
previous papers we have introduced additional structure into this construction,
namely an action of symmetries, which is related to fixing renormalisation
conditions. This action characterizes anomalies and satisfies a cocycle
condition which is summarized in the unitary anomalous Master Ward identity.
Here (using perturbation theory) we show how this cocycle condition is related
to the Wess-Zumino consistency relation and the consistency relation for the
anomaly in the BV formalism, where the latter is the generalized Jacobi
identity for the associated $L_\infty$-algebra.

Keywords:

*none*