For theories with mixed topological, holomorphic, and ordinary spacetime dimensions, OPE coefficients are proposed to be sheaf cohomology classes, with singular derived coefficients appearing under explicit dimension-counting conditions.
Superconformal algebras and holomorphic field theories
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abstract
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.
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On coefficients of operator product expansions for quantum field theories with ordinary, holomorphic, and topological spacetime dimensions
For theories with mixed topological, holomorphic, and ordinary spacetime dimensions, OPE coefficients are proposed to be sheaf cohomology classes, with singular derived coefficients appearing under explicit dimension-counting conditions.