[Paper Review] Lectures on Celestial Holography

Ana-Maria Raclariu|arXiv (Cornell University)|Jul 5, 2021

Black Holes and Theoretical Physics88 references57 citations

TL;DR

The notes review how the subleading soft graviton theorem enhances Lorentz symmetry to Virasoro in 4D asymptotically flat gravity, formulate celestial amplitudes as S-matrices in a boost-eigenstate basis, and survey celestial symmetries and their constraints on scattering.

ABSTRACT

These notes consist of 3 lectures on celestial holography given at the Pre-Strings school 2021. We start by reviewing how semiclassically, the subleading soft graviton theorem implies an enhancement of the Lorentz symmetry of scattering in four-dimensional asymptotically flat gravity to Virasoro. This leads to the construction of celestial amplitudes as $\mathcal{S}$-matrices computed in a basis of boost eigenstates. Both massless and massive asymptotic states are recast as insertions on the celestial sphere transforming as global conformal primaries under the Lorentz SL$(2, \mathbb{C})$. We conclude with an overview of celestial symmetries and the constraints they impose on celestial scattering.

Motivation & Objective

• Review the connection between soft theorems and asymptotic symmetries in four-dimensional asymptotically flat spacetimes.
• Construct celestial amplitudes as S-matrices in a basis of boost eigenstates with massless and massive states as conformal primaries.
• Explain how celestial symmetries constrain and organize scattering, including three- and four-point functions and OPE data.

Proposed method

• Analyze the subleading soft graviton theorem and derive Virasoro-like Ward identities for the S-matrix.
• Define conformal primary wavefunctions for massless and massive states and construct celestial amplitudes as integrals/transformations of standard S-matrix elements.
• Use Penrose diagrams and Bondi gauge to discuss asymptotic symmetries (extended BMS and superrotations).
• Introduce Milne slicing and an AdS3-inspired integral representation to realize conformal primaries.
• Compute a tree-level celestial amplitude with two massless and one massive scalar as an explicit example.
• Discuss how celestial symmetry currents constrain amplitudes and fix certain three-point functions.

Experimental results

Research questions

• RQ1 How does the subleading soft graviton theorem encode an infinite-dimensional enhancement of Lorentz symmetry to Virasoro in 4D gravity?
• RQ2 How can scattering in asymptotically flat spacetimes be reformulated as celestial amplitudes on the celestial sphere?
• RQ3 What constraints do celestial symmetries (Poincaré, conformal, and soft currents) impose on celestial three- and four-point functions and OPE coefficients?
• RQ4 How do massless and massive asymptotic states appear as conformal primaries, and how are their celestial amplitudes computed?
• RQ5 What is the role and structure of the 2D stress-tensor-like object arising from soft graviton modes?

Key findings

• Subleading soft graviton theorem implies Virasoro enhancement of the Lorentz symmetry in the S-matrix.
• Celestial amplitudes are defined as S-matrices in a basis of boost eigenstates, with massless and massive states mapped to conformal primaries on the celestial sphere.
• A 2D stress tensor constructed from a subleading soft graviton mode yields Ward identities for celestial correlators, mirroring CFT structures.
• Poincaré symmetry fixes celestial three-point functions and constrains four-point functions; soft theorems fix leading OPE coefficients for gluons and gravitons.
• There exists an infinite set of soft currents in celestial theories, with calculable algebras shown in examples.