Symmetry group at future null infinity I: Scalar theory

TL;DR

This paper studies the symmetry structure of massless scalar fields at future null infinity, revealing a rich algebra of flux operators that may relate to Carrollian geometry and broader field theories.

Contribution

It introduces a method to derive symmetry generators at null infinity and identifies their algebra, including a divergent central charge, linking scalar theory to Carrollian geometry.

Findings

Derived Poincaré flux operators at null infinity.

Identified a closed symmetry algebra with a divergent central charge.

Connected the algebra to the geometry of Carrollian manifolds.

Abstract

We reduce the massless scalar field theory in Minkowski spacetime to future null infinity. We compute the Poincar\'e flux operators, which can be generalized and identified as the supertranslation and superrotation generators. These generators are shown to form a closed symmetry algebra with a divergent central charge. In the classical limit, we argue that the algebra may be interpreted as the geometric symmetry of a Carrollian manifold, i.e., the hypersurface of future null infinity. Our method may be used to find more physically interesting Carrollian field theories.