Extended Super BMS Algebra of Celestial CFT

TL;DR

This paper explores the supersymmetric extension of BMS symmetry in celestial CFT for supergravity and Yang-Mills, revealing an infinite-dimensional superalgebra structure and its relation to soft theorems.

Contribution

It constructs fermionic conformal primaries, derives their OPEs, and demonstrates the supersymmetric extension of BMS algebra in celestial CFT.

Findings

Supercharges form an infinite-dimensional supersymmetry algebra.

Soft theorems relate bosonic and fermionic operators via Ward identities.

Supertranslation operators decompose into holomorphic and anti-holomorphic supercurrents.

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.