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Extended Super BMS Algebra of Celestial CFT

Angelos Fotopoulos, Stephan Stieberger, Tomasz R. Taylor, Bin Zhu

Abstract

We study two-dimensional celestial conformal field theory describing four-dimensional ${\cal N}=1$ 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 supersymmetry algebra. The algebra of $\mathfrak{sbms}_4$ 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.

Extended Super BMS Algebra of Celestial CFT

Abstract

We study two-dimensional celestial conformal field theory describing four-dimensional 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 supersymmetry algebra. The algebra of 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.

Paper Structure

This paper contains 20 sections, 211 equations, 19 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. Supermultiplets
  4. OPEs of fermion fields in supersymmetric EYM theory
  5. Soft gaugino
  6. Soft gravitino, supercurrent and SUSY Ward identities
  7. OPEs of super BMS generators
  8. $TS$
  9. $SP$ and $\bar{S}P$
  10. $S\bar{S}$ and relation to the supertranslation operator ${\cal P}$
  11. $SS$ and $\bar{S}\bar{S}$
  12. The algebra $\mathfrak{sbms}_4$ of super $BMS_4$ generators
  13. Conclusions
  14. Soft and collinear limits of gauginos and gravitinos
  15. Soft gaugino limit
  16. ...and 5 more sections

Figures (19)

  • Figure 1: Feynman diagrams leading to soft gaugino singularities.
  • Figure 2: Feynman diagrams leading to soft gaugino singularities.
  • Figure 3: Double wavy line represents the graviton
  • Figure 4: Virtual graviton decaying into a gaugino pair.
  • Figure 5: The double wavy-solid line represents the gravitino decaying into a gauge boson and gaugino.
  • ...and 14 more figures