Superconformal algebras and holomorphic field theories

TL;DR

This paper demonstrates that four-dimensional superconformal algebras, when holomorphically twisted, reveal an infinite-dimensional structure related to known holomorphic quantum field theories, connecting higher symmetries with two-dimensional chiral algebras.

Contribution

It establishes a novel link between 4D superconformal algebras and infinite-dimensional holomorphic symmetry algebras, extending the understanding of their structure and relation to 2D chiral theories.

Findings

Holomorphic twist yields infinite-dimensional derived enhancements of superconformal algebras.

Identifies connections between these algebras and known holomorphic QFT symmetry algebras.

Shows how deformations relate to Koszul resolutions and central extensions in chiral algebras.

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.