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Double-soft limit and celestial shadow OPE from charge bracket

Daniele Pranzetti, Domenico Giuseppe Salluce

TL;DR

This work connects celestial OPEs with asymptotic phase-space charges, using a charge bracket correspondence to resolve the double-soft ambiguity in the mixed-helicity sector and to compute shadow celestial OPEs. By enforcing the OPE/bracket relationship across gravity and Yang-Mills, the authors establish a canonical first-entry-soft-first prescription and develop an algorithm that handles shadow transforms consistently, including dual and shadow operators. They organize conformal primaries via celestial diamonds, test the procedure on the energy-momentum tensor, and extend to shadow OPEs in both gravity and YM, finding that shadow/dual OPEs share the same structure up to nonlocal kernels. The results advance flat-space holography by providing a practical, symmetry-consistent framework to derive shadow OPEs and to analyze the interplay between soft theorems, higher-spin charges, and celestial CFT algebras.

Abstract

The dual formulations of an infinite tower of tree-level soft theorems in asymptotically flat spacetimes for scattering amplitudes in the standard energy-momentum basis and for correlators of a 2D celestial conformal field theory imply a correspondence between the celestial operator product expansion (OPE) and the higher spin charge bracket. We apply such correspondence to provide first a prescription to solve the double-soft limit ambiguity in the mixed-helicity sector of celestial OPEs. Furthermore, demanding the charge OPE/bracket correspondence to remain valid when operators are shadow transformed, we construct an algorithm to compute shadow celestial OPEs. We first test the algorithm by recovering results in the previous literature involving the celestial energy-momentum tensor; we then apply it to both gravity and Yang-Mills theory and generalize the OPE derivation to arbitrary spins.

Double-soft limit and celestial shadow OPE from charge bracket

TL;DR

This work connects celestial OPEs with asymptotic phase-space charges, using a charge bracket correspondence to resolve the double-soft ambiguity in the mixed-helicity sector and to compute shadow celestial OPEs. By enforcing the OPE/bracket relationship across gravity and Yang-Mills, the authors establish a canonical first-entry-soft-first prescription and develop an algorithm that handles shadow transforms consistently, including dual and shadow operators. They organize conformal primaries via celestial diamonds, test the procedure on the energy-momentum tensor, and extend to shadow OPEs in both gravity and YM, finding that shadow/dual OPEs share the same structure up to nonlocal kernels. The results advance flat-space holography by providing a practical, symmetry-consistent framework to derive shadow OPEs and to analyze the interplay between soft theorems, higher-spin charges, and celestial CFT algebras.

Abstract

The dual formulations of an infinite tower of tree-level soft theorems in asymptotically flat spacetimes for scattering amplitudes in the standard energy-momentum basis and for correlators of a 2D celestial conformal field theory imply a correspondence between the celestial operator product expansion (OPE) and the higher spin charge bracket. We apply such correspondence to provide first a prescription to solve the double-soft limit ambiguity in the mixed-helicity sector of celestial OPEs. Furthermore, demanding the charge OPE/bracket correspondence to remain valid when operators are shadow transformed, we construct an algorithm to compute shadow celestial OPEs. We first test the algorithm by recovering results in the previous literature involving the celestial energy-momentum tensor; we then apply it to both gravity and Yang-Mills theory and generalize the OPE derivation to arbitrary spins.

Paper Structure

This paper contains 36 sections, 33 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Higher spin charges and their action
  4. Gravity
  5. Yang-Mills theory
  6. Celestial diamonds
  7. Double-soft limit
  8. Shadow OPE in gravity
  9. Energy-momentum tensor
  10. Same-helicity sector
  11. Mixed-helicity sector
  12. Shadow OPE in Yang--Mills
  13. Same-helicity sector
  14. Mixed-helicity sector
  15. Conclusions
  16. ...and 21 more sections

Figures (2)

  • Figure 1: Celestial diamond associated with negative-helicity soft gravitons with (\ref{['fig:CD-GR-2']}) $s = 0, 1$ and (\ref{['fig:CD-GR-1']}) $s\geq 2$.
  • Figure 2: Celestial diamond associated with negative-helicity soft gluons with (\ref{['fig:CD-YM-2']}) $s = 0$ and (\ref{['fig:CD-YM-1']}) $s\geq1$.