Open Questions
1: Can one compute loop corrections to soft theorems in non-abelian gauge theories using celestial holography?
HINT: The non-abelian soft current is fully known (from conventional calculations) at two loops, and partially at three loops.
– Lorenzo Magnea
2: What replaces the semiclassical description of spacetime near a black hole singularity, and how is it described holographically?
HINT: First decide if black holes have a conventional interior.
– Gary Horowitz
3: What is the relationship, if any, between asymptotic symmetries and generalized symmetries, e.g. higher form/higher group/noninvertible symmetries, of gauge theories and gravity?
HINT: Higher form symmetries are abelian and probably can’t capture the full structure of asymptotic symmetries, but it would be interesting to see if there are connections to higher group symmetries.
– Temple He
4: Does the holographic behavior of gravity arise from the constraints, and if so, does constructing the holographic map rely on their solution, i.e. on first having a description of bulk evolution?
HINT: Try to give a systematic construction of the holographic map, e.g. in AdS.
– Steve Giddings
5: What is the global form of infinite-dimensional conservation laws for a black hole in asymptotically flat spacetime?
HINT: They should be derived from a matching between the black hole’s horizon charges and asymptotic symmetry charges at the different boundaries.
– Laura Donnay
6: Do the large pure gauge/diffeomorphism profiles have their own dynamics and in what sense are they holographic?
HINT: The large pure gauge/diffeomorphism profiles allow for additional bulk field configurations to be summed over, which amounts to promoting the profiles themselves to quantum fields living on the boundary.
– Anonymous
7: Find observable memory effects corresponding to w_{1+\infty} symmetries of celestial holography.
8: Find memory observables corresponding to black hole horizon symmetries (of course one can think about displacement of test masses, but no experimenter would buy that!).
HINT: Contact author for hints and possible collaboration!
– Ali Seraj
9: In string theory, is there a direct relation between celestial OPEs and the OPEs of the associated worldsheet OP-vertex operators?
– Anonymous
10: Find and prove the best possible upper bound on the asymptotic complexity of computing a tree-level n-gluon (or n-graviton) amplitude.
HINT: Answering this question may require or enable the discovery of a completely new formulation of the problem.
– Marcus Spradlin
11: What is the celestial analog of a Ryu-Takayanagi surface?
– Anonymous
12: How can we relate the various definitions of charges in extended BMS existing in GR literature to the behavior of asymptotic probes? In particular, how do we distinguish the various definitions of angular momentum and angular momentum flux found in the literature using asymptotic inertial detectors?
– Massimo Porrati
13: Gravity is non-renormalizable as a QFT. How does the study of asymptotic symmetries and celestial OPE depend on its UV completion? Does this study give us any clue about the nature of UV completion ? Or is it independent of it?
– Laurent Freidel
14: Can one predict an observable which is a direct consequence of the subleading structure of soft theorems/memories/symmetries and design a protocol to observe it in the coming years?
HINT: The leading order displacement memory effect is on the way to be observed.
– Geoffrey Compere
15: How are gravitational bulk subregions encoded in (celestial) CFT and what is an associated physical observable?
HINT: In AdS/CFT the entanglement structure of the CFT knows about bulk geometry.
– Ana-Maria Raclariu
16: How does BFSS fit into the framework of celestial holography?
HINT: There have been several recent works exploring soft theorems in BFSS, which clarify the manifestation of certain symmetries.
– Jordan Cotler
17: Do gravitons exist? If yes, are they elementary or composite?
HINT: Gravitational waves, Weinberg-Witten’s theorem.
– Tomasz Taylor
18: What are the symmetry algebras of gauge theories and gravity at the quantum level?
– Andrea Puhm
19: Does one expect a holographic dual to flat space that is fully decoupled from gravity? In how many dimensions does it live and what are its locality properties?
HINT: String- theoretical realization of/insights into flat holography?
– Monica Guica
20: Do the *high energy* (higher spin) symmetries of flat space string scattering amplitudes (Gross) have a nice realisation in terms of the conformal symmetries of the celestial sphere?
HINT: The Stieberger-Taylor approach to string scattering amplitudes suggests a close relation between the worldsheet and the celestial sphere and perhaps there is a relation to the W_{infty} higher spin symmetry of the free worldsheet theory (leading one to further ask what, if any, is the relation to the soft W_{infty} or to the tensionless limit of AdS_3/CFT_2 ?)
– Rajesh Gopakumar
21: Certain theories in asymtoptically flat space–such as gravity coupled to a CFT–do not have the S-matrix as a well-defined observable. Boundary observables still exist, such as energy correlators. How should we think about the celestial hologram for such theories?
– Nima Arkani-Hamed
22: How can we see celestial amplitudes in low energy (e.g. LHC) data? Does decoupling of UV physics from low-energy amplitudes manifest here?
– Massimo Porrati
23: Generalize Hawking’s Lorentzian computation of black hole radiance in gravitational collapse spacetimes to include the effect of soft modes, in three stages:
- For free fields
- For interacting fields (tree level), including the nonlinear interactions that excite memory
- Somehow include the effect of secularly growing fluctuations in black hole charges
Then, fix a cut of future null infinity at some retarded time u after the Page time, and trace over soft modes including the edge modes associated with that cut.
See if this tracing is enough to remove entanglement between internal Hawking quanta and external Hawking quanta (as it would for a GHZ like state), following suggestion of arXiv:1706.07143.
– Eanna Flanagan
24: What is the celestial CFT state dual to black holes?
– Andrea Puhm
25: How should we define (the analogue of) the entanglement wedge for arbitrary spacetimes?
– Anonymous
26: Is there a ”self-dual sector” of AdS/CFT?
– Akshay Yelleshpur Srikant
27: What microscopic physical principle(s) that aren’t visible in semiclassical gravity (analogous to boundary unitarity and locality in AdS/CFT) should constrain the celestial CFT?
HINT: This seems to me to be the key ingredient if celestial holography is supposed to be a flat space version of AdS/CFT rather than just a flat space version of Brown-Henneaux. Obviously, the S matrix should be unitary but I don’t see anything beyond that.
– Geoffrey Penington
28: Are large gauge charge conserving amplitudes in non-abelian gauge theory always free of IR divergences? Can they usefully define unitary IR finite s-matrix?
HINT: Analogous statements held in QED and gravity.
– Anonymous
29: There is a strong suspicion that without supersymmetry, we should not be able to find exactly flat space solutions in quantum gravity–the cosmological constant problem. The string landscape is argued to let us to get a “discretum” with arbitrarily small CC without SUSY, but not exactly zero. What does celestial holography say about this? What if anything is special about supersymmetric theories given that the celestial boundary of flat space is automatic in this program?
– Nima Arkani-Hamed
30: How does the Planck length emerge out of a celestial CFT with finite central charge?
HINT: Planck’s length is the only scale at asymptotic infinity. It’s unclear how/if it can be related to a nonzero, finite dimensionless central charge.
– Roberto Emparan
31: What are the unitarity/causality constraints on amplitudes in various formalisms?
– Massimo Porrati
32: What celestial CFT reproduces the one-loop exact all-plus amplitudes of self-dual gravity?
HINT: Bulk self-duality is related to boundary chirality.
– Anonymous
33: How much further progress can be achieved in the asymptotic approach to classical and quantum gravity by (i) using a double null foliation and (ii) by deriving the bracket structure from first/action principles?
– Glenn Barnich
34: Can black hole entropy be computed directly from the string theory (or other UV complete theory) path integral, S-matrix, or other on-shell quantity, without recourse to low energy effective field theory?
HINT: The action for the Schwarzschild solution comes entirely from a boundary term at infinity.
– Per Kraus
35: How can translationally-invariant spacetime emerge from a celestial CFT with only unbroken Lorentz invariance?
– Anonymous
36: One thing I’m curious about is the interplay between the celestial developments and the 2-body problem in GR. Could any of the infinite dimensional celestial symmetry algebras help in this problem? Is there a celestial counterpart of the analytic continuation from open to bounded orbits?
– Miguel Campiglia
37: Can gravitational waveforms be computed from correlations functions in a two-dimensional conformal field theory? To what precision, in what expansion (post-Newtonian, post-Minkowski, self-force, post-background,…) and how easily?
– Anonymous
38: What is the most general form of the four graviton scattering amplitude consistent with all known symmetries and constraints?
HINT: Constraints include those arising from unitarity, crossing, towers of soft theorems and black hole production at high energies.
– Andy Strominger
39: What makes unitarity of the S-matrix obvious in celestial holography?
– Nima Arkani-Hamed
40: Can the study of infrared physics in QCD and the array of soft theorems give us new insight on the mechanism for confinement?
HINT: Confinement is an infrared phenomena, classical and quantum IR divergences suggest that one should look at Infrared QCD and its goldstone physics in a new light.
– Laurent Freidel
41: What are the celestial CFT axioms?
– Andrea Puhm
42: How can Celestial Holography help bridge results from Amplitudes, the Conformal Bootstrap and It from Qubit?
– Sabrina Pasterski
43: Is the W_{1+\infty} symmetry partially preserved, spontaneously broken, or explicitly broken at the quantum level?
HINT: The answer to this question might depend on what space of state we apply it to. Scattering states versus well behaved wave packets for instance.
– Laurent Freidel
44: Aside from the uplift of N=8 self-dual supergravity, does there exist an anomaly-free variant of Poisson-Chern-Simons theory on twistor space?
– Roland Bittleston
45: Is the tree-level Einstein S matrix the only consistent asymptotically flat n graviton S matrix (i.e. only poles and no cuts) that does not include pole exchange contributions from particles of arbitrarily high spin? Do the tree level n graviton Einstein, Type II and Heterotic S matrices constitute an exhaustive listing of such S matrices once we drop the constraint on the spins of exchange poles?
HINT:
– “Consistent” means respecting all relevant general physical principles.
– A has been established for 4-graviton scattering assuming a constraint on growth of tree level S matrices with energy (CRG conjecture). Exercise: Prove CRG and extend to n-point scattering.
– Either a proof or counterexample would be interesting. Note that
- a) Tree-level Type II/ Heterotic graviton S matrices on $R^4 \times CY$ are universal (independent of the CY).
- b) May be useful to systematically study warped compactifications that have the dilaton as a modulus.
– Shiraz Minwalla
46: Do non-supersymmetric holographic dualities exist?
HINT: Celestial holography has become a ripe arena for answering this through work on integrable theories, self-dual sectors, topological and N = 2 strings, etc.
– Atul Sharma
47: What is the complete spectrum, including single-particle operators, multi-particle operators, and descendants, that one can extract from (tree-level) correlation functions?
HINT: One way could be implementing the partial wave expansion for a generic n-point diagram and directly starting from momentum space (instead of doing Mellin transforms first) might be easier.
– Anonymous
48: What timelike boundaries are allowed in four-dimensional cosmology – motivated by genericity of such topology and by holography – and what are observational bounds on their presence within our horizon?
HINT: From the bottom up, for some cases Dirichlet (fixed intrinsic boundary geometry) evidently make sense, while in the general case conformal boundary conditions (fixing the trace of the extrinsic curvature and the conformal class of the metric) appears better behaved; from the top down this is UV sensitive (being a short scale feature) and requires further investigation in string theory.
– Eva Silverstein
49: Some initial data will lead to Black-Hole creation at the classical level. How does this process affects the amplitudes, soft theorems and symmetry action and celestial OPE’s?
HINT: Dig deeper in connection between OPE and asymptotic symmetry in the presence of black holes.
– Laurent Freidel
50: Can we add Black Holes to CCFT dynamically?
HINT: Compute Black Hole microstates.
– Lucadam Ciamball
51: (How) Do the symmetry algebras extend beyond the single helicity sector?
– Andrea Puhm
52: What are all the non-trivially acting symmetries of nature?
HINT: At tree level, they include the loop group of W1+∞.
– Anonymous
53: Is it possible to derive celestial holography in terms of quantum information theory?
HINT: Progress can be borrowed from AdS3/CFT2, e.g. tensor networks for estimating entanglement entropy. Klein signature could help.
– Alfredo Guevara Gonzalez
54: What is the most promising method for detecting a memory effect?
HINT: Consider all fundamental forces: gravitational, electromagnetic, strong, and perhaps even weak.
– David Nichols
55: Is there a clean fingerprint of unstable massive particles, important in the UV [such as massive string modes at weak string coupling, super-planckian black hole microstates], on celestial amplitudes?
– Nima Arkani-Hamed
56: What is the simplest top-down model of celestial holography that isn’t self-dual?
HINT: Is the asymptotically flat part of the bulk four or higher dimensional? If the bulk theory is a string theory, does the celestial dual admit a perturbative expansion as well as a 1/N expansion? Can it be obtained as a limit of AdS/CFT, perhaps in Mellin space?
– David Skinner
57: How does the SO(4,2) conformal group act on celestial amplitudes and soft symmetries?
HINT: See Chen, Myers and Raclaria for relevant observations.
– Anonymous
58: Is there a local two dimensional Euclidean quantum field theory that calculates soft exchange and soft emission (at each order in perturbation theory) in four dimensional non-abelian gauge theory?
HINT: The answer is yes for abelian gauge theory and gravity, and the form of the lower dimensional models is fixed by (asymptotic) symmetries.
– Daniel Kapec
59: What is the exact role of timelike infinity (i^+ and i^-) in flat space holography?
– Marc Henneaux
60: Is the universality of the tower of logarithmic soft theorems a consequence of asymptotic symmetries of the S-matrix?
– Sangmin Choi
61: How do W1+∞ soft symmetries act on the Love numbers of a Kerr black hole?
HINT: Understand how black holes can source the W1+∞ charges.
– Anonymous
62: Standard AdS/CFT relates certain AdS_4 supergravity/string theories to ABJM theories: what truncations/adjustments need to be made to reduce this to the self-dual sector? (and to Carollian and celestial limits?)
– Lionel Mason
63: Is there a celestial dual of the Schwarzschild black hole, and how do we describe it?
– Bin Zhu
64: How does the non-commutativity of the consecutive soft limits in the mixed helicity sector get reflected in the (soft) symmetry algebra of GR?
– Shamik Banerjee
65: Which types of boundary conditions (finite or asymptotic) on a UV-complete gravitational/string theory do we expect to give rise to a holographic dual description? Under which conditions do we expect this holographic dual to (i) obey the usual rules of quantum mechanics (ii) be unitary and (iii) have a suitable notion of locality?
– Jan de Boer
66: To what extent can the rules of quantum field theory be written in a manifestly gauge invariant way? (e.g. in terms of field strengths rather than potentials). If this cannot be done, is there a simple way to say what the obstruction to doing so is?
– David Garfinkle
67: It has been suggested by Vafa and collaborators that there is a dark fifth dimension whose size is several microns. How could this be incorporated in celestial holography?
– John H. Schwarz
In a recent paper JHEP 01(2024) 085 (Unified treatment of null and spatial infinity IV: angular momentum at null and spatial infinity) Neev Khera and I raised this point See discussion around footnote 4 on p25. That was based on some results of Mohamed, Prabhu and Kroon who began a rigorous analysis of the existence of solutions with properties that are needed to ensure conservation of supermomentum. A month ago Lydia Bieri told me of some recent work (she has completed but is in the process of writing) that is more conclusive than Mohamed et al. She analyzes data in which –in contrast to Christodoulou-Klainnerman– the mass aspect at spatial infinity is not spherically symmetric. She finds that generically, conditions at scri plus and scriminus that are necessary for conservation of supermomentum are not satisfied. As you know, I had pointed out that the conservation with CK initial data is of a trivial sort because in those space-times, the flux of supermomentum across scri plus and scri minus vanish identically –so it is a bit like conservation of angular momentum in spherically symmetric systems! we need the data of the type Lydia considers.
As we say in the footnote, this is a fertile area for further work.
Another recent result is that scriplus is a Weakly Isolated Horizon and all its standard properties emerge from the WIH framework (Horizons and Null infinity: A Fugue in 4 voices, Phys. Rev. D109, L061501 (2024); and Null Infinity as a Weakly Isolated Horizon arXiv:2402.17977 ). An issue
that would be of interest in the near future:
68: What is the relation between what happens at scriplus and at the final dynamical horizon in binary mergers?
– Abhay Ashtekar
69: Are BMS_4 symmetries composite?
HINT: Infinite-dimensional symmetries sometimes can be (Sugawara-)decomposed into more fundamental building blocks (like Kac-Moody currents for Virasoro, BMS_3 or W_N symmetries). Something analogous could be possible for BMS_4 and might help us to constrain scattering amplitudes, count Kerr black hole microstates, sharpen statements regarding asymptotic symmetries, etc.
– Daniel Grumiller
70: What sets the scale of the EM memory effect? If there is a physical displacement, what sets the scale?
In our discussion of the FK S-matrix in
https://arxiv.org/pdf/2211.15712.pdf
it appears it would have to be some asymptotically soft scale – is this a fundamental scale of the theory?
– Raju Venugopalan
71: Do we really expect flat space holography to give us a duality describing the full UV structure of the bulk physics or just the infrared part of it?
– Francisco Javier Rojas Fernandez
72: If so, like in AdS/CFT, could we find what is the expansion parameter that takes us away from field theory into more stringy effects?
– Francisco Javier Rojas Fernandez
73: Is there a top-down construction of a 2d theory which is holographically dual to self-dual gravity (potentially coupled to other fields) on a self-dual black hole background?
– Simon Heuveline
74: The celestial OPEs for gluons and gravitons can be derived from the Mellin transforms of the soft collinear gluon and graviton singularities, respectively. The symmetry algebras associated with gluon and graviton OPEs are the S and w_{1+\infty} algebras, respectively.
– Igor Mol