Symmetries of the celestial supersphere

Abstract We study the celestial CFT dual to theories with bulk supersymmetry. The boundary theory realizes supersymmetry in the spirit of the Green–Schwarz superstring: there is manifest 4 d super-Poincaré symmetry, but no 2 d superconformal symmetry. Nevertheless, we can extend the celestial sphere itself to a supermanifold—the celestial supersphere. This provides a unified framework for describing key features of celestial holography, including conformally soft theorems, OPEs, and chiral soft algebras. Using these tools, we demonstrate that the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="fraktur">b</mml:mi> <mml:mi mathvariant="fraktur">m</mml:mi> <mml:mi mathvariant="fraktur">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mn mathvariant="fraktur">4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> algebra extends to a novel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="fraktur">s</mml:mi> <mml:mi mathvariant="fraktur">b</mml:mi> <mml:mi mathvariant="fraktur">m</mml:mi> <mml:mi mathvariant="fraktur">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mn mathvariant="fraktur">4</mml:mn> <mml:mrow> <mml:mo mathvariant="fraktur" stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">N</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> algebra. We also relate the supersymmetric <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">L</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="fraktur">w</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> <mml:mo>∧</mml:mo> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> algebra to Hamiltonian vector fields on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">N</mml:mi> </mml:mrow> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , consistent with the expectation from twistor theory, and deduce the deformation of this algebra by a cosmological constant, Λ. These results are all universal and independent of the specific details of the underlying theory.