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Journal Article

Superconformal algebras and holomorphic field theories


Williams,  Brian R.
Max Planck Institute for Mathematics, Max Planck Society;

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Saberi, I., & Williams, B. R. (2023). Superconformal algebras and holomorphic field theories. Annales Henri Poincaré, 24(2), 541-604. doi:10.1007/s00023-022-01224-7.

Cite as: https://hdl.handle.net/21.11116/0000-000B-3FF9-7
We show that four-dimensional superconformal algebras admit an
infinite-dimensional derived enhancement after performing a holomorphic twist.
The type of higher symmetry algebras we find are closely related to algebras
studied by Faonte-Hennion-Kapranov, Hennion-Kapranov, and the second author
with Gwilliam in the context of holomorphic QFT. We show that these algebras
are related to the two-dimensional chiral algebras extracted from
four-dimensional superconformal theories by Beem and collaborators; further
deforming by a superconformal element induces the Koszul resolution of a plane
in $\mathbb{C}^2 \cong \mathbb{R}^4$. The central charges at the level of
chiral algebras arise from central extensions of the higher symmetry algebras.