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.
Unravelling the Holomorphic Twist: Central Charges
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The holomorphic twist provides a powerful framework to study minimally protected sectors in supersymmetric quantum field theories. We investigate the algebraic structure underlying the holomorphic twist of $\mathcal{N} = 1$ superconformal field theories in four dimensions. In particular, in holomorphically twisted theories the flavour and conformal symmetry algebras are enhanced to infinite-dimensional higher Kac Moody and higher Virasoro symmetry algebras respectively. We explicitly compute the binary and ternary $\lambda$-brackets and clarify their relation with the underlying infinite-dimensional symmetry algebra. Doing so we show that the central extensions of said symmetry algebras precisely encode the conformal anomalies $a$ and $c$ as well as the flavour central charges of the physical four-dimensional theory. This parallels the familiar story in two dimensions where the conformal anomaly $c$ is encoded in the central extension of the Virasoro algebra.
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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.