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A Comment on Loop Corrections to the Celestial Stress Tensor

Sabrina Pasterski

TL;DR

The paper analyzes loop corrections to the celestial stress tensor within flat-space holography, focusing on the subleading soft graviton. It shows that the 1-loop IR-divergent correction to the subleading soft theorem can be recast as a quadratic correction to soft charges derived from the BMS flux algebra, aligning amplitude-based results with covariant phase-space constructions. By integrating the BMS flux framework and celestial diamond structure with soft dressings, the work clarifies how non-linear vacua and IR dressing organize celestial operators into symmetry-consistent CCFT representations. This strengthens the bridge between amplitudes, celestial CFT, and asymptotic symmetries, providing a coherent, symmetry-protected account of loop-level gravitational soft dynamics.

Abstract

In this note we show how the 1-loop exact correction to the subleading soft graviton theorem arising from IR divergences of scattering amplitudes matches onto the quadratic corrections to the soft charges computed from the BMS flux algebra. In the process, we examine how the BMS flux construction extends the celestial diamond framework to non-linear order and non-trivial vacua, and provides the natural symmetry generators for Celestial CFT.

A Comment on Loop Corrections to the Celestial Stress Tensor

TL;DR

The paper analyzes loop corrections to the celestial stress tensor within flat-space holography, focusing on the subleading soft graviton. It shows that the 1-loop IR-divergent correction to the subleading soft theorem can be recast as a quadratic correction to soft charges derived from the BMS flux algebra, aligning amplitude-based results with covariant phase-space constructions. By integrating the BMS flux framework and celestial diamond structure with soft dressings, the work clarifies how non-linear vacua and IR dressing organize celestial operators into symmetry-consistent CCFT representations. This strengthens the bridge between amplitudes, celestial CFT, and asymptotic symmetries, providing a coherent, symmetry-protected account of loop-level gravitational soft dynamics.

Abstract

In this note we show how the 1-loop exact correction to the subleading soft graviton theorem arising from IR divergences of scattering amplitudes matches onto the quadratic corrections to the soft charges computed from the BMS flux algebra. In the process, we examine how the BMS flux construction extends the celestial diamond framework to non-linear order and non-trivial vacua, and provides the natural symmetry generators for Celestial CFT.
Paper Structure (8 sections, 64 equations, 1 figure, 1 table)

This paper contains 8 sections, 64 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. BMS Flux Algebra
  3. A Bondi Gauge Primer
  4. BMS Fluxes
  5. A 1-Loop Correction to the Stress Tensor
  6. Reviewing the Loop Corrected Soft Graviton
  7. The Soft S-Matrix
  8. Discussion

Figures (1)

  • Figure 1: Goldstone (red) and memory (black) diamonds for the leading (a) and subleading (b) soft graviton theorem.