Extended super BMS algebra of celestial CFT

Abstract

We study two-dimensional celestial conformal field theory describing four- dimensional $$ \mathcal{N} $$ 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 super- symmetry algebra. The algebra of $$ {\mathfrak{sbms}}_4 $$ 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.

Massive celestial fermions

“…(4.17) This is consistent with the massless wavefunctions in [5], where they were used to study supersymmetry on the CCFT, up to differences between our conventions for the Dirac equation and the conventions in [27].…”

“…We compute the Dirac inner product of two conformal primary wavefunctions to demonstrate that they are delta function normalizable as long as we consider the principal continuous series ∆ = 1 + iλ for λ ∈ R. We note that there are two choices for a complete basis: J = 1 2 or J = − 1 2 and λ ∈ R or J = ± 1 2 and λ ∈ R +∪0 . Finally we compute the massless limit and show it is in agreement with the spinor solutions in [5]. In section 5 we derive the spin− 1 2 momentum generators in the celestial basis and show that they are not diagonal and that they form a representation of the Poincaré algebra along with the Lorentz generators.…”

“…We demand that the Dirac conformal primaries are delta function normalizable with respect to the Dirac inner product. Such a normalization was also considered in [5]. We look at the X 0 = 0 Cauchy slice where this inner product is given by…”

“…The conformal primary basis was introduced in [1,2] for amplitudes containing massless and massive scalars, photon and graviton fields. It has since been extended to all massless fields in [3][4][5]. This construction was then generalized to massive bosons in [6].…”

Relativistic partial waves for celestial amplitudes

“…theorems familiar from Minkowski space amplitudes correspond to so called conformal soft theorems for celestial amplitudes, which were studied in [22][23][24][25][26][27][28][29][30]. The representation of BMS symmetry generators on the celestial sphere, and other aspects such as OPE expansions of celestial operators were discussed in [31][32][33][37][38][39][40]. Information contained at past boundary of future null infinity concerning local excitations in an asymptotically flat bulk space-time has been investigated in [34].…”