Twistorial chiral algebras in higher dimensions

TL;DR

This paper extends the concept of chiral algebras from four-dimensional gauge theories and gravity to higher dimensions that are multiples of four, revealing new structures in twistor space and their relation to soft symmetries.

Contribution

It introduces higher-dimensional chiral algebras associated with integrable sectors of gauge theory and gravity, generalizing known 4D results using twistor sigma models.

Findings

Chiral algebras exist in higher dimensions as in 4D.

These algebras are linked to soft symmetry algebras in collinear limits.

Chiral structures are defined on the 2-sphere in higher dimensions.

Abstract

In four spacetime dimensions, the classically integrable self-dual sectors of gauge theory and gravity have associated chiral algebras, which emerge naturally from their description in twistor space. We show that there are similar chiral algebras associated to integrable sectors of gauge theory and gravity whenever the spacetime dimension is an integer multiple of four. In particular, the hyperk\"ahler sector of gravity and the hyperholomorphic sector of gauge theory in $4m$-dimensions have well-known twistor descriptions giving rise to chiral algebras. Using twistor sigma models to describe these sectors, we demonstrate that the chiral algebras in higher-dimensions also arise as soft symmetry algebras under a certain notion of collinear limit. Interestingly, the chiral algebras and collinear limits in higher-dimensions are defined on the 2-sphere, rather than the full celestial sphere.