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Description
The holomorphic twist provides a powerful method for extracting exact data from general 4d 𝒩=1 QFTs. I will introduce the holomorphic twist and explain how the twisted theory acquires an infinite-dimensional symmetry algebra, and is endowed with the structure of a “higher” VOA. Its full operator product structure can be encoded in a collection of n-ary λ-brackets, which generate the positive modes of the higher VOA and assemble into a homotopic Lie conformal algebra. I will show how these λ-brackets can be translated back into physical OPE data, and in particular how the anomalies of the original 4d theory are cleanly reflected in the holomorphic. When the parent theory has extended supersymmetry, the twisted theory gains extra structure: for 4d 𝒩=2 SCFTs, a further twist recovers the familiar VOA associated to the theory. Throughout the talk I will illustrate the formalism through concrete examples ranging from gauge theories to non-Lagrangian Argyres-Douglas theories. Time permitting, I will end with a brief outlook on current developments and open directions, including computational tools for λ-brackets and connections to factorisation algebras and bootstrap-style constraints.
