2024 Simons Collaboration on Celestial Holography Annual Meeting

The first annual meeting of the Simons Collaboration in Celestial Holography (CH) was held on April 11–12th, 2024, with 142 in-person participants and an additional 14 remote participants. In addition to the speakers, the meeting was attended by CH PIs and postdoctoral fellows, distinguished faculty members working on related topics, and many other graduate students and postdocs. The meeting was immediately preceded by a two-day satellite meeting (April 9–10th), held at the Andaz hotel, featuring 14 stimulating talks with topics ranging from the mathematics of chiral algebras and top-down stringy models of celestial holography, to a detailed overview of short- and long-term prospects for the experimental observation of gravitational memory effects. At the annual meeting, there were also 13 posters presented by graduate students, which became the focal point for many active discussions during the breaks between plenary talks, as well as after the final talk.

The annual meeting kicked off with collaboration director Andrew Strominger (Harvard University) giving an overview of approaches, successes, and both short- and long-term goals for the collaboration. He reviewed the deep connections between Weinberg’s soft theorems, memory effects and asymptotic symmetries that have been developed by his group, which initially galvanized the subject. Collaboration goals ranged from the complete determination of the symmetries of asymptotically flat spacetimes to the construction of toy models from string theory, and prospects for experimental detection of memory effects. He paid particular emphasis to the bottom-up approach to CH, by which one can deduce properties of the putative celestial dual from known scattering processes. This approach is universal, independent of any special stringy realization or concomitant assumptions of a celestial holographic duality, and therefore suitable for revealing broad lessons about quantum gravity including in our own universe. He also highlighted crowdsourced questions for inspiring future work on CH from collaboration members, affiliates and colleagues, which are now available on the collaboration website.

Ana-Maria Raclariu (University of Amsterdam) explained how one can take flat-space limits of observables in the much-studied AdS/CFT correspondence to reproduce and explain various exotic features of celestial amplitudes describing the scattering of massless particles. She included a beautiful alternative derivation of the infinite tower of symmetries recently discovered in CH from this approach, exhibiting the potential of realizing a celestial CFT within a higher-dimensional CFT which itself participates in an AdS/CFT duality.

Shiraz Minwalla (Tata Institute of Fundamental Research) explained his recent tour-de-force work describing a formulation of (a generalization of) the S-matrix realized as a functional of boundary values. This approach generalizes the study of local singularities called “bulk point singularities” from AdS to flat spacetimes, and generalizing the analysis to include multi-bulk point singularities. His construction has potentially fascinating ramifications for understanding emergent bulk locality in asymptotically flat spacetimes.

Natalie Paquette (University of Washington), a collaboration PI, reviewed the twistorial approach to 4D amplitudes and asymptotic symmetries pioneered by herself and fellow PI Costello, which has been used recently to construct a top-down example of a CH duality from string theory. She then presented new results, including the first determination of a fully quantum-corrected asymptotic symmetry algebra, including deformations at all loops. In 4D, this provides an all-orders result for collinear splitting functions in a version of QCD coupled to special choices of matter.

Atul Sharma (Harvard University), a collaboration postdoc, described a celestial CFT dual for MHV amplitudes in gauge theory by coupling a certain large-N chiral algebra to Liouville theory. He emphasized a novel structure called leaf amplitudes as a natural celestial quantity and explained how they can be recombined to understand unusual distributional features of standard celestial amplitudes.

Geoffrey Compere (Université Libre de Bruxelles) resolved a fundamental puzzle in the definition of asymptotically flat spacetimes by explaining how the five asymptotic boundaries of flat spacetime could be consistently joined in a manner compatible with a single action of the BMS group, which encodes the asymptotic symmetries general relativity. His construction accommodated logarithmic corrections to soft theorems and was used to derive celestial conserved charges. He also explained generalizations and challenges for de Sitter spacetimes.

Lionel Mason (Oxford University), a collaboration PI, provided a pedagogical overview of key aspects of the twistorial formulation of massless physics on flat spacetimes and explained how twistorial methods generalize to spacetimes with nonvanishing cosmological constant. He used this approach to derive a deformation of the W-algebra obtained by Strominger, et al., for AdS spacetimes. In addition, Mason explained work in progress connecting infinite towers of celestial charges obtained by Friedel (collaboration PI) and others to integrable hierarchies which are manifest on twistor space.

Andrea Puhm (University of Amsterdam), a collaboration PI, explored a logarithmic class of quantum corrections to soft theorems in scalar QED and general relativity (GR). She demonstrated that these subleading effects were universal, much like the vaunted leading soft theorems in QED and GR. Moreover, she provided a first-principles derivation that these corrections correspond to genuine asymptotic symmetries associated to conserved charges.

Geoffrey Compère
Université Libre de Bruxelle
Progress on the Definition of Asymptotically Flat and de Sitter Spacetimes
View Slides (PDF)

The definition of scattering in asymptotically flat spacetimes requires to consistently match its five asymptotic boundaries: past/future timelike and null infinities and spatial infinity. I will present a framework consistent with logarithmic corrections to soft theorems where a single BMS group acts on all boundaries and where individual ingoing/outgoing bodies are ascribed initial/final BMS charges. Using the post-Minkowskian expansion, I will demonstrate that non-radiative regions are entirely characterized by a set of conserved celestial charges that consist of the Geroch-Hansen multipole moments, the generalized BMS charges and additional non-stationary multipole moments. In the context of asymptotically de Sitter spacetimes, I will finally demonstrate that the presence of a quadrupole moment of any localized source in de Sitter leads to a fluctuating boundary metric that breaks the conjectured conformal asymptotic symmetry group. Dynamical Einstein gravity in de Sitter cannot therefore be modelled by a 3d CFT.

Lionel Mason
University of Oxford
Twistor Approaches to Celestial Symmetries and their AdS Deformations
View Slides (PDF)

This talk will review the twistor origins of celestial symmetry algebras and their extension to AdS. It will go on to discuss connections with the integral systems literature and top-down approaches to celestial holography via twistor actions and chiral sigma models and (ambi-)twistor strings.

Shiraz Minwalla
Tata Institute of Fundamental Research
The S-Matrix and Boundary Correlators in Flat Space

We consider the path integral of a quantum field theory in Minkowski spacetime with fixed boundary values (for the elementary fields) on asymptotic boundaries. We define and study the corresponding boundary correlation functions obtained by taking derivatives of this path integral with respect to the boundary values. The S-matrix of the QFT can be extracted directly from these boundary correlation functions after smearing. We interpret this relation in terms of coherent state quantization and derive the constraints on the path-integral as a function of boundary values that follow from the unitarity of the S-matrix. We then study the locality structure of boundary correlation functions. In the massive case, we find that the boundary correlation functions for generic locations of boundary points are dominated by a saddle point which has the interpretation of particles scattering in a small elevator in the bulk, where the location of the elevator is determined dynamically, and the S-matrix can be recovered after stripping off some dynamically determined but non-local “renormalization” factors. In the massless case, we find that while the boundary correlation functions are generically analytic as a function on the whole manifold of locations of boundary points, they have special singularities on a sub-manifold, points on which correspond to light-like scattering in the bulk. We completely characterize this singular scattering sub-manifold and find that the corresponding residues of the boundary correlations at these singularities are precisely given by S-matrices. This analysis parallels the analysis of bulk-point singularities in AdS/CFT and generalizes it to the case of multi-bulk point singularities.

Natalie Paquette
University of Washington
Associativity is Enough
View Slides (PDF)

I will report on work to appear shortly with my student, Victor Fernandez. The celestial chiral algebras of “twistorial” theories, 4d theories with local holomorphic lifts to twistor space, are associative even at the quantum level. In this work, we use elementary considerations, such as symmetries and associativity, to find closed-form expressions for all coefficients (i.e., at arbitrary loop order) of the OPEs for the celestial chiral algebras associated to twistorial theories, in particular self-dual Yang-Mills theory coupled to special choices of matter; similar considerations apply also for self-dual general relativity coupled to a special matter sector. This work constitutes a preliminary step in a program proposed by Costello and myself called the chiral algebra bootstrap, in which correlation functions for such chiral algebras can be used to compute higher loop form factors in non-supersymmetric 4d quantum field theories.

Andrea Puhm
University of Amsterdam
Asymptotic Symmetries and Log Soft Theorems in Gauge Theories and Gravity
View Slides (PDF)

Key to a celestial holographic correspondence is the identification of all symmetries. Perturbative quantum gravity was shown to be governed by the infinite-dimensional $w_{1+\infty}$ symmetry which arises from the tower of tree-level soft graviton theorems. How do quantum (loop) effects affect the classical (tree-level) symmetry interpretation? Aside from the leading soft theorems which are all-loop exact, subleading ones receive quantum corrections with logarithmic dependence on the energy of the soft particle. In this talk, I will initiate a program to compute quantum corrections to the charges that generate the asymptotic symmetries in scalar QED and perturbative quantum gravity and show that their conservation corresponds precisely to the leading universal logarithmic soft theorems. I will comment on the fate of the $w_{1+\infty}$ symmetry algebra at the quantum level.

Ana-Maria Raclariu
King’s College London & University of Amsterdam
What Can We Learn About Celestial Holography from Ads/CFT?

It is well known that perturbative scattering amplitudes in Minkowski spacetime can be obtained from a flat space limit of AdS-Witten diagrams. Moreover, certain conjectured properties of scattering amplitudes can be derived in a related limit from known properties of CFT correlation functions. In most cases, these results concern the scattering of massive particles. In this talk, I will show that many properties of massless celestial amplitudes similarly arise in certain kinematic limits of correlation functions of local, unitary CFTs in one higher dimension. I will present some concrete examples of celestial amplitudes constructed in this way and derive the infinity of celestial symmetries from Ward identities in the higher dimensional CFT.

Atul Sharma
Harvard University
A Celestial Dual for MHV Amplitudes
View Slides (PDF)

Atul Sharma will describe recent work on coupling a large-N chiral algebra to the semiclassical limit of Liouville theory to reproduce 4D gluon MHV amplitudes as correlators of 2D light operators. The correlators will produce certain building blocks called “leaf amplitudes”, and Sharma will explain how to recombine them into standard translationally invariant celestial amplitudes.

Andy Strominger
Harvard University
Celestial Holography: Past, Present and Future
View Slides (PDF)

The ongoing endeavor to realize the holographic principle for quantum gravity in nearly asymptotically flat spacetimes like the one we inhabit is described and motivated. Some highlights of this endeavor are presented, along with some open questions.