Revisiting the Shadow Stress Tensor in Celestial CFT

TL;DR

This paper refines the celestial stress tensor construction in celestial CFT, addressing an obstruction in the double soft limit and exploring the implications for symmetries and operator product expansions.

Contribution

It proposes a modified definition of the celestial stress tensor that overcomes previous obstructions and extends the basis beyond the conformally soft sector.

Findings

Resolved the double soft limit obstruction in celestial stress tensor

Extended the celestial basis to include non-soft sectors

Analyzed how basis choice affects symmetry realization in OPEs

Abstract

We revisit the standard construction of the celestial stress tensor as a shadow of the subleading conformally soft graviton. In its original formulation there is an obstruction to reproducing the expected TT OPE in the double soft limit. We propose a modification to the definition which circumvents this obstruction and then extend this change of basis beyond the conformally soft and single helicity sectors. In the process we investigate how (non)-commutativity of double soft limits is tied to the decoupling of primary descendants, and how our choice of celestial basis determines which symmetries are manifest at the level of the OPE beyond the MHV sector.