Extended super BMS algebra of celestial CFT
Angelos Fotopoulos, Stephan Stieberger, Tomasz R. Taylor, Bin Zhu
Abstract
A bstract We study two-dimensional celestial conformal field theory describing four- dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> =1 supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of BMS symmetry. We construct fermionic conformal primary wave functions and show how they are related via supersymmetry to their bosonic partners. We use soft and collinear theorems of supersymmetric Einstein-Yang- Mills theory to derive the OPEs of the operators associated to massless particles. The bosonic and fermionic soft theorems are shown to form a sequence under supersymmetric Ward identities. In analogy with the energy momentum tensor, the supercurrents are shadow transforms of soft gravitino operators and generate an infinite-dimensional super- symmetry algebra. The algebra of $$ {\mathfrak{sbms}}_4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>sbms</mml:mtext> <mml:mn>4</mml:mn> </mml:msub> </mml:math> generators agrees with the expectations based on earlier work on the asymptotic symmetry group of supergravity. We also show that the supertranslation operator can be written as a product of holomorphic and anti-holomorphic supercurrents.