Appears in collection : Higher Structures in Holomorphic and Topological Field Theory

In symplectic geometry the notion of a moment map encodes beautifully the idea of a symmetry of a mechanical system. In the Batalin-Vilkovisky formalism there is a parallel notion to the moment map that encodes a homological version of Noether’s theorem. BV quantization of this moment map encodes the current algebras of QFT, and it provides a useful perspective on some familiar anomalies, including the Adler-Bardeen-Jackiw anomaly. This talk will discuss these ideas and introduce some examples from the setting of holomorphic field theories, recently developed with B.Williams. In particular, we will describe a systematic generalization of the affine Lie algebras and connect with work of Faonte-Hennion-Kapranov.