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

Understand

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.