Physics

Gravitation

Pure mathematics

Symmetry (geometry)

Mathematics

Mathematical physics

Graviton

Algebra over a field

Gauge symmetry

Gauge theory

Geometry

Theoretical physics

Quantum mechanics

Subalgebra

Homogeneous space

Journal of High Energy Physics

All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.

Holographic symmetry algebras for gauge theory and gravity