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Implications of Superrotations

Sabrina Pasterski

TL;DR

Pasterski develops a unified infrared framework tying together asymptotic symmetries, soft theorems, and memory effects in asymptotically flat spacetimes. By proving a Ward identity for superrotations from the subleading soft graviton theorem, she establishes a semiclassical Virasoro structure for 4D gravity and introduces a spin memory observable. She then constructs a 2D stress tensor from the soft sector and formulates a map from 4D scattering to a celestial CFT using conformal primary wavefunctions, illustrating how 4D S-matrix data can be reinterpreted as 2D conformal correlators. Together, these results illuminate the infrared structure of quantum gravity, reveal vacuum transition and memory phenomena, and propose a concrete path toward flat space holography via a celestial CFT, while highlighting subtleties in the non-compact symmetry and basis choices.

Abstract

A framework of connections between asymptotic symmetries, soft theorems, and memory effects has recently shed light on a universal structure associated with infrared physics. Here, we show how this pattern has been used to fill in missing elements. After the necessary groundwork, we begin by proving a Ward identity for superrotations using the subleading soft graviton theorem, thereby demonstrating a semiclassical Virasoro symmetry for scattering in quantum gravity. Next, we show there exists a new spin memory effect associated with this symmetry, explain more generally how the connections between the vertices of the infrared triangle predicted this, and describe what other examples and variations have been unveiled. Taking to heart this newly motivated Virasoro symmetry, we review how the soft theorem has been recast as a Virasoro Ward identity for a putative two dimensional conformal field theory. This derivation relies upon a map from plane wave scattering states to a conformal primary basis, which we then construct. We provide examples of familiar scattering amplitudes recast in this basis and discuss the somewhat exotic nature of the putative CFT2. We conclude by describing ongoing efforts to tame some of these features and what this change of basis in turn has taught us about the infrared limit which began our story.

Implications of Superrotations

TL;DR

Pasterski develops a unified infrared framework tying together asymptotic symmetries, soft theorems, and memory effects in asymptotically flat spacetimes. By proving a Ward identity for superrotations from the subleading soft graviton theorem, she establishes a semiclassical Virasoro structure for 4D gravity and introduces a spin memory observable. She then constructs a 2D stress tensor from the soft sector and formulates a map from 4D scattering to a celestial CFT using conformal primary wavefunctions, illustrating how 4D S-matrix data can be reinterpreted as 2D conformal correlators. Together, these results illuminate the infrared structure of quantum gravity, reveal vacuum transition and memory phenomena, and propose a concrete path toward flat space holography via a celestial CFT, while highlighting subtleties in the non-compact symmetry and basis choices.

Abstract

A framework of connections between asymptotic symmetries, soft theorems, and memory effects has recently shed light on a universal structure associated with infrared physics. Here, we show how this pattern has been used to fill in missing elements. After the necessary groundwork, we begin by proving a Ward identity for superrotations using the subleading soft graviton theorem, thereby demonstrating a semiclassical Virasoro symmetry for scattering in quantum gravity. Next, we show there exists a new spin memory effect associated with this symmetry, explain more generally how the connections between the vertices of the infrared triangle predicted this, and describe what other examples and variations have been unveiled. Taking to heart this newly motivated Virasoro symmetry, we review how the soft theorem has been recast as a Virasoro Ward identity for a putative two dimensional conformal field theory. This derivation relies upon a map from plane wave scattering states to a conformal primary basis, which we then construct. We provide examples of familiar scattering amplitudes recast in this basis and discuss the somewhat exotic nature of the putative CFT2. We conclude by describing ongoing efforts to tame some of these features and what this change of basis in turn has taught us about the infrared limit which began our story.

Paper Structure

This paper contains 22 sections, 187 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Asymptotically Flat Spacetimes
  3. Null Infinity
  4. Coordinate-Free Definition
  5. Bondi Expansion
  6. The Scattering Problem
  7. Soft Theorems
  8. Mode Expansions
  9. Superrotations
  10. Ward Identity
  11. Spin Memory
  12. A $U(1)$ Example
  13. Gravitational Displacement Memory
  14. A New Gravitational Memory
  15. Vacuum Transitions
  16. ...and 7 more sections

Figures (3)

  • Figure 1: The IR Triangle. There exists a series of universal connections within infrared physics, which we are tasked to explain, exploit, and expand upon herein.
  • Figure 2: Penrose diagram for Minkowski space, represented as a patch of the Einstein static universe and unwrapped with antipodal points shown. Massless trajectories travel at $45^\circ$ angles and enter and exit at $\mathcal{I}^\pm$. Geodesics for massive particles enter at $i^-$ and exit at $i^+$.
  • Figure 3: Diagrammatic expansion of an amplitude with an extra gauge boson as its energy is tuned towards zero. The leading contributions come from the soft gauge boson attaching to the external lines.