Conformally Soft Fermions

TL;DR

This paper extends the framework of celestial conformal field theory to include fermionic soft charges, revealing infinite-dimensional fermionic symmetries and their role in celestial amplitudes and asymptotic symmetries.

Contribution

It constructs fermionic charge operators in 2D celestial CFT from 4D bulk fields, extending soft theorems to fermionic sectors and completing the celestial symmetry pyramid.

Findings

Fermionic soft charges generate infinite-dimensional fermionic symmetries.

Construction of fermionic charge operators from 4D bulk fields.

Identification of conformally soft gravitino and photino operators in celestial CFT.

Abstract

Celestial diamonds encode the global conformal multiplets of the conformally soft sector, elucidating the role of soft theorems, symmetry generators and Goldstone modes. Upon adding supersymmetry they stack into a pyramid. Here we treat the soft charges associated to the fermionic layers that tie this structure together. This extends the analysis of conformally soft currents for photons and gravitons which have been shown to generate asymptotic symmetries in gauge theory and gravity to infinite-dimensional fermionic symmetries. We construct fermionic charge operators in 2D celestial CFT from a suitable inner product between 4D bulk field operators and spin $s=\frac{1}{2}$ and $\frac{3}{2}$ conformal primary wavefunctions with definite SL(2,$\mathbb{C}$) conformal dimension $\Delta$ and spin $J$ where $|J|\leq s$. The generator for large supersymmetry transformations is identified as the conformally soft gravitino primary operator with $\Delta=\frac{1}{2}$ and its shadow with $\Delta=\frac{3}{2}$ which form the left and right corners of the celestial gravitino diamond. We continue this analysis to the subleading soft gravitino and soft photino which are captured by degenerate celestial diamonds. Despite the absence of a gauge symmetry in these cases, they give rise to conformally soft factorization theorems in celestial amplitudes and complete the celestial pyramid.