Deformed $w_{1+\infty}$ Algebras in the Celestial CFT

TL;DR

The paper investigates how non-minimal bulk couplings modify the celestial CFT's soft-current symmetry, revealing a deformation of the wedge $w_{1+
ext{infty}}$ algebra. By formulating light-transformed currents $W^{q,s}$, it derives generalized brackets that depend on coupling constants and color factors, and shows that Jacobi identities impose strong relations among these couplings. The deformed algebra closely matches $w_{1+
ext{infty}}$ but is not identical to $W_{1+
ext{infty}}$, with scalar currents required for closure in several cases and potential loop-induced central extensions. Additionally, the authors find that one-loop all-plus amplitudes do not alter the algebra, suggesting a close tie to the self-dual sector, while full deformation likely requires non-self-dual dynamics or scalar content. Overall, the work clarifies the symmetry structure of CCFT under higher-derivative interactions and maps constraints that any consistent non-minimal theory must satisfy at the level of soft currents.

Abstract

We compute the modification of the $w_{1+\infty}$ algebra of soft graviton, gluon and scalar currents in the celestial CFT due to non-minimal couplings. We find that the Jacobi identity is satisfied only when the spectrum and couplings of the theory obey certain constraints. We comment on the similarities and essential differences of this algebra to $W_{1+\infty}$.