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Symmetries of holomorphic QFT and the higher dimensional Kac-Moody algebras

By Owen Gwilliam

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.

Information about the video

  • Date of recording 1/14/19
  • Date of publication 1/28/19
  • Institution IHES
  • Format MP4

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