Celestial 1-form symmetries

TL;DR

This paper explores the extension of the $S$-algebra to an infinite-dimensional 1-form symmetry algebra in self-dual Yang-Mills theory, linking it to integrability and celestial holography.

Contribution

It demonstrates that in self-dual Yang-Mills, the $S$-algebra enhances to a 1-form symmetry algebra with implications for celestial holography.

Findings

The $S$-algebra extends to an infinite-dimensional 1-form symmetry algebra.

The 2-form currents encode integrability and hierarchies of self-dual Yang-Mills.

Equality of Carrollian corner charges and celestial chiral algebra modes is established.

Abstract

The $S$-algebra originally arose as a chiral algebra of asymptotic symmetries of Yang-Mills theory. We show that in the self-dual sector of Yang-Mills, the $S$-algebra gets upgraded to an infinite-dimensional algebra of $1$-form symmetries in the bulk. The associated 2-form currents encode the integrability and hierarchies of self-dual Yang-Mills. As an application, we prove the equality of Carrollian corner charges with modes of the celestial chiral algebra by expressing them as integrals of the same 2-form currents over homologous 2-cycles.