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

TL;DR

This paper investigates how non-minimal couplings modify the $w_{1+ abla}infty$ algebra in celestial CFT, revealing constraints for algebra consistency and comparing it to $W_{1+ abla}infty$.

Contribution

It provides the first detailed analysis of the deformed $w_{1+ abla}infty$ algebra due to non-minimal couplings in celestial CFT, highlighting conditions for algebraic consistency.

Findings

Jacobi identity constrains spectrum and couplings

Modified algebra differs from $W_{1+ abla}infty$ in key aspects

Conditions for consistent algebra are identified

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 $W_{1+\infty}$.