Soft Algebras in AdS 4 from Light Ray Operators in CFT 3

Abstract Flat Minkowski space (M 4 ) and AdS 4 can both be conformally mapped to the Einstein cylinder. The maps may be judiciously chosen so that some null generators of the I + boundary of M 4 coincide with antipodally-terminating null geodesic segments on the boundary of AdS 4 . Conformally invariant nonabelian gauge theories in M 4 have an asymptotic S -algebra generated by a tower of soft gluons given by weighted null line integrals on I + . We show that, under the conformal map to AdS 4 , the leading soft gluons are dual to light transforms of the conserved global symmetry currents in the boundary CFT 3 . The tower of light ray operators obtained from the S O ( 3 , 2 ) descendants of this light transform realize a full set of generators of the S -algebra in the boundary CFT 3 . This provides a direct connection between holographic symmetry algebras in M 4 and AdS 4 .