On Effective Field Theories with Celestial Duals

TL;DR

This paper demonstrates that associativity constraints in celestial CFTs lead to specific restrictions on bulk coupling constants, affecting scattering amplitudes and revealing a deformed $w_{1+ fty}$ symmetry algebra.

Contribution

It establishes a connection between celestial CFT associativity and bulk theory constraints, extending previous algebraic results to amplitude behavior and symmetry deformations.

Findings

Four-point amplitudes from holomorphic or anti-holomorphic three-point amplitudes vanish under constraints.

Purely holomorphic or anti-holomorphic higher-point amplitudes also vanish.

Constraints align with the Jacobi identity-derived conditions from prior work.

Abstract

We show that associativity of the tree-level OPE in a celestial CFT imposes constraints on the coupling constants of the corresponding bulk theory. These constraints are the same as those derived in arXiv:2111.11356 from the Jacobi identity of the algebra of soft modes. The constrained theories are interesting as apparently well-defined celestial CFTs with a deformed $w_{1+\infty}$ symmetry algebra. We explicitly work out the ramifications of these constraints on scattering amplitudes involving gluons, gravitons and scalars in these theories. We find that all four-point amplitudes constructible solely from holomorphic or anti-holomorphic three-point amplitudes vanish on the support of these constraints, which implies that all purely holomorphic or purely anti-holomorphic higher-point amplitudes vanish.