Twistors and celestial holography

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In summary: Thomas Witten, Andrew Strominger, Christof Koch (2016) Witten, Strominger, and Koch describe how a "topological string" in supertwistor space can explain a number of compressed formulas for Feynman diagrams in Yang-Mills theory. The use of twistor variables, with and without strings, is now standard in "amplitudeology", the quest to find the hidden reasons why amplitudes in gauge theory have all these unexpected properties. "The AdS/CFT connection" by Robert Mason, Andrew Strominger, and Dimitry Lukyanov (2016) Mason, Strominger, and Lu
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mitchell porter

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Twistors are central to "celestial" holography in flat space
Many of us have heard of "twistors", arguably Roger Penrose's biggest contribution to theoretical physics. Twistor space is a space which maps nonlocally onto physical space-time; in particular, lightlike structures in space-time, like null lines and light cones, become much more "local" in twistor space. For various reasons, Penrose thought that twistor space was possibly a more fundamental arena for theoretical physics than space-time, and for many years he and a hardy band of mostly British collaborators worked to re-describe particle physics in terms of twistors. Equations of massless particles become very simple in twistor space, because of their scale invariance; promising for physics, since all the elementary particles in the standard model are fundamentally massless.

In the 21st century, twistors got a second boost when Witten discovered that a "topological string" in supertwistor space, could explain a number of remarkably compressed formulas for Feynman diagrams in Yang-Mills theory. The use of twistor variables, with and without strings, is now standard in "amplitudeology", the quest to find the hidden reasons why amplitudes in gauge theory have all these unexpected properties. Many stalwarts of the twistor program (Hodges, Mason, Skinner) are central to these studies.

In the title, I also mention "celestial holography". Holographic duality is probably familiar to most modern readers of theoretical physics; one hears incessantly about "AdS/CFT duality", how "gravity in the AdS bulk" is holographically equivalent to a non-gravitational CFT "on the boundary"; also how anti de Sitter space is different from our universe's space-time, but that the duality still has some practical uses in condensed matter physics.

AdS/CFT has been celebrated as an explicit realization of the holographic principle that quantum gravity should behave like a quantum field theory in one less dimension, but people have still hoped to find a form of the holographic principle suitable for flat space. After all, the first glimpse of the principle was Hawking and Bekenstein's inference that the entropy of a black hole should be proportional to its surface area, not its volume. And in fact, a kind of flat-space holography has been taking shape in recent years, under the name of celestial holography.

In astronomy, the celestial sphere does for the sky, what a globe does for the Earth's surface in geography. It is a two-dimensional sphere on which all celestial phenomena can be depicted; each object located according to where in the sky it is seen, when viewed from Earth. Celestial holography implements the holographic principle in this framework: physics throughout a three-dimensional space, is described by a field theory confined to the two spatial dimensions of the celestial sphere.

The main theorist behind celestial holography has probably been Andrew Strominger, whose background is in string theory, but who has approached this topic from a more general perspective of quantum gravity. Strominger has done a lot of work on "soft" symmetries at infinity, in which there are new conserved quantities arising from the presence of arbitrary numbers of zero-energy gravitons radiating away (this extends to gravity, earlier work by Steven Weinberg on "soft pions"); this briefly came to public attention just before Stephen Hawking died, when it was claimed that the quantum information apparently lost during Hawking radiation, is actually preserved in these soft degrees of freedom.

Frankly I understand very little about celestial holography, except the bare idea of a celestial CFT being equivalent to a gravitational theory in flat space, and that some of the unexpected symmetries discovered in amplitudeology, are related to the symmetries of the celestial CFT. But it's apparent that the twistors are at work here too. It makes sense - the structure of twistor space is related to the asymptotic structure of physical space-time - recall how twistor objects correspond to lightlike entities, like light cones.

What prompts me to make this post, is the appearance in the past few months of numerous papers indicating advances in twistor theory, or celestial holography, or both. But I'll begin with an older review of twistor theory that I found:

"Twistors and amplitudes" by Andrew Hodges (2015)

"Penrose's definition of twistors can be considered as doing for the conformal group what spinors do for the Lorentz group", Hodges writes at the start of part 3. Hodges himself is best known for discovering "momentum twistors", a twistor space for momentum variables rather than position variables, an extremely simple idea which opened the door to many of the discoveries in the era of the twistor string.

All right, so what are some of these recent papers that caught my attention? These are quite technical works. It's like we've arrived in the middle of the lecture and don't know everything that led up to this. But we'd better take notes and try to understand anyway, if we don't want to get left behind. :-)

"Top-down holography in an asymptotically flat spacetime" by Kevin Costello, Natalie Paquette, Atul Sharma

This paper proposes a concrete example of celestial holography: a specific 4d field theory, including gravity, and a specific 2d celestial dual. The 4d theory was actually described in a paper last year by Costello (who seems to be a leader in turning the "physicists' math" of quantum field theory into something acceptable to real mathematicians), as an example of a very rare class of quantum field theories whose space-time properties are fixed by their being local in twistor space. The fields themselves are not obviously reminiscent of anything we know from real life: an SO(8)-valued four-dimensional "WZW model", coupled to a "Kähler scalar". What may be significant, is just that a theory whose construction can be motivated by the twistor research program, happens to yield an example of celestial holography.

Meanwhile, one of the problems faced by twistor theory, arises from what was originally supposed to be a virtue: there is a natural chirality to twistor theory, in the sense that opposite chiralities are described differently, and one more naturally than the other. Penrose thought this might help to explain parity violation in the weak force. But it also means that there is a kind of bias in the twistorial description of four-dimensional Yang-Mills theory and gravity: it's easier to describe the "self-dual" part of those fields, rather than the "anti-self-dual" part (I hope I have that right). The duality in question refers to duality under the Hodge star operator, a kind of orthogonality operation in vector spaces. Four dimensions is unique in that the Hodge dual of a 2d object is itself a 2d object, and so something can be self-dual, its own dual; or anti-self-dual, the latter meaning that the dual is the original times -1.

One may approach this situation in different ways. One may, for example, use "ambitwistors", which combine twistors with dual twistors. Or one may embrace the asymmetry; we have been discussing "chiral" theories of gravity in a few other threads, recently.

But in any case, within twistor theory, one of the longstanding challenges is to describe the "nonlinear graviton", which seems to be a graviton containing a quantum of space-time curvature. A few years back, Penrose himself proposed doing this by patching together algebras of flat-space twistor field operators (analogous to the overlapping coordinate patches which appear in Riemannian geometry), in an approach called palatial twistor theory (because it was inspired by a conversation with the mathematician Michael Atiyah, that took place near Buckingham Palace). And now we have:

"Quantizing the non-linear graviton" by Roland Bittleston, Atul Sharma, David Skinner

Once again we have a kind of field that only specialists know about - "holomorphic Poisson-BF theory". But that's the field on twistor space; when we transform to physical space-time, it turns into the self-dual part of general relativity. The theory turns out to be anomalous. In physical space-time, such anomalies mean that a field theory is badly defined. But if the anomalies occur in twistor space, it just means that the space-time theory loses one of its classical symmetries (and it loses the nice property of integrability). However, the twistor anomalies can be canceled by the addition of a new field, which in space-time manifests as "a type of axion" (not the QCD axion, but one with analogous couplings) which also appeared in the twistor string.

The appearance of a new scalar is reminiscent of the previous paper by Costello et al; and there's even an author in common, Atul Sharma.

"Moyal deformations, W_{1+∞} and celestial holography" by Wei Bu, Simon Heuveline, David Skinner

"Celestial chiral algebras, colour-kinematics duality and integrability" by Ricardo Monteiro

These papers are about celestial holography: specifically, two kinds of algebra, w algebra and its quantum deformation, W algebra, which are expected to appear on both sides of some celestial dualities. On the 2d, celestial side, they should appear as algebraic relations among the operators of the celestial CFT; on the 4d side, they will show up as relations among the scattering amplitudes dual to the celestial operators. In other words, they are a bridge between amplitudeology and celestial holography.

In these two papers, one may also see, again, the emphasis on self-dual Yang-Mills and self-dual gravity, i.e. something less than the full gauge and gravity theories of the real world. The "double copy" relation between gauge theory and gravity also shows up in the second paper.

I haven't studied these papers at all.

"Soft Gravitons in the BFSS Matrix Model" by Noah Miller, Andrew Strominger, Adam Tropper, Tianli Wang

Here Strominger returns to his roots, and sets the stage for celestial holography within string theory, by looking for soft gravitons in flat-space M-theory. The BFSS matrix model is a sector of string theory in which everything consists of webs of strings connecting pointlike D0-branes, and the soft gravitons are found to correspond to certain small sub-webs ("matrix subblocks whose rank is held fixed... in the large-N limit", see Figure 2).
 
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OK, so what does it all mean? After all, it's not the standard model. There's nothing here that will satisfy people wanting a new model for the real world right away.

However, one may view this as progress of a mathematical kind, that one hopes will eventually make contact with the real world. In learning quantum field theory, one may learn about individual equations like Klein-Gordon and Dirac equations, and then eventually one learns how to combine them in a realistic Yang-Mills-Higgs theory. Similarly, here field theories are being constructed and studied in an interestingly holistic way: defined on twistor space as well as on physical space-time, and possessing a celestial holographic dual whose symmetries are also present in the scattering amplitudes of the 4d theory. If and when we can do that for the standard model, it will be a whole new level of understanding.

My main concern is the continuing centrality of self-duality. Perhaps some new idea is needed to extend these relationships, to the non-self-dual part of realistic theories.

One more speculative remark. In the final paper, by Strominger et al, regarding the difference between hard gravitons and soft gravitons, it is written: "This is reminiscent of the large-N limit of QCD, where baryons have masses of order N and mesons of order 1. It would be interesting to see how far this analogy can be pushed."

Five years ago, there was a speculative paper

"Confinement and fractional charge of quarks from braid group approach to holographic principle" by Janusz Jacak

which suggested that a proton, with its three fractionally charged quarks, might be holographically dual to braided anyons on the celestial sphere. Perhaps it gives us a glimpse of a future holographic standard model, in which baryons and mesons, quarks and gluons, and branes and strings, are all different perspectives on the same reality.
 
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mitchell porter said:
Five years ago, there was a speculative paper

"Confinement and fractional charge of quarks from braid group approach to holographic principle" by Janusz Jacak

which suggested that a proton, with its three fractionally charged quarks, might be holographically dual to braided anyons on the celestial sphere. Perhaps it gives us a glimpse of a future holographic standard model, in which baryons and mesons, quarks and gluons, and branes and strings, are all different perspectives on the same reality.

any connection with this ?

A topological model of composite preons​


Sundance O. Bilson-Thompson

We describe a simple model, based on the preon model of Shupe and Harari, in which the binding of preons is represented topologically. We then demonstrate a direct correspondence between this model and much of the known phenomenology of the Standard Model. In particular we identify the substructure of quarks, leptons and gauge bosons with elements of the braid group B3. Importantly, the preonic objects of this model require fewer assumed properties than in the Shupe/Harari model, yet more emergent quantities, such as helicity, hypercharge, and so on, are found. Simple topological processes are identified with electroweak interactions and conservation laws. The objects which play the role of preons in this model may occur as topological structures in a more comprehensive theory, and may themselves be viewed as composite, being formed of truly fundamental sub-components, representing exactly two levels of substructure within quarks and leptons.


Comments:6 pages, 4 figures, added info about hypercharge, lepton number
Subjects: High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)
Report number:ADP-05-05/T615
Cite as:arXiv:hep-ph/0503213
 
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kodama said:
any connection with this ?

A topological model of composite preons​

Jacak wants to get a proton from three quarks, Bilson-Thompson wants to get quarks and leptons from three subquarks (preons). A variety of attempts have been made to embed Bilson-Thompson's idea in a working theory, the most I can say is that braiding of holographic anyons represents another arena in which one could try to make it work.

There was another paper yesterday on amplitudes from celestial holography

"Towards Gravity From a Color Symmetry" by Alfredo Guevara

which seems to be saying that momentum in four dimensions is holographically equivalent on the celestial sphere to a U(∞) symmetry (i.e. unitary matrix with infinitely many rows and columns), which is weird, but might be similar to holography in the BFSS matrix model of M theory.
 
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mitchell porter said:
Jacak wants to get a proton from three quarks, Bilson-Thompson wants to get quarks and leptons from three subquarks (preons). A variety of attempts have been made to embed Bilson-Thompson's idea in a working theory, the most I can say is that braiding of holographic anyons represents another arena in which one could try to make it work.

There was another paper yesterday on amplitudes from celestial holography

"Towards Gravity From a Color Symmetry" by Alfredo Guevara

which seems to be saying that momentum in four dimensions is holographically equivalent on the celestial sphere to a U(∞) symmetry (i.e. unitary matrix with infinitely many rows and columns), which is weird, but might be similar to holography in the BFSS matrix model of M theory.
could braided anyons on the celestial sphere serve as Bilson-Thompson preons?
 
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btw
Twistors are central to "celestial" holography in flat space any relevant to Woit
 
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could this be combined with octonions for 3 generation ?
 
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kodama said:
could braided anyons on the celestial sphere serve as Bilson-Thompson preons?
kodama said:
btw
Twistors are central to "celestial" holography in flat space any relevant to Woit
kodama said:
could this be combined with octonions for 3 generation ?
1. A simpler but relevant question would be, what kind of 4d theory do you get from "celestial anyons"? I see nothing directly tackling this question, and don't understand enough about celestial CFTs to reason it out by myself. But there are a few works that might be relevant, I'll post something if I achieve any insights.

2. There's an "infinity twistor" which shows up in twistor theory when scale invariance is broken, e.g. when you have mass, or when you have gravity. I'd look at graviweak unification from this perspective.

3. The appearance of SO(8) in Costello et al (see #1) could be something octonionic.
 
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mitchell porter said:
1. A simpler but relevant question would be, what kind of 4d theory do you get from "celestial anyons"? I see nothing directly tackling this question, and don't understand enough about celestial CFTs to reason it out by myself. But there are a few works that might be relevant, I'll post something if I achieve any insights.

2. There's an "infinity twistor" which shows up in twistor theory when scale invariance is broken, e.g. when you have mass, or when you have gravity. I'd look at graviweak unification from this perspective.

3. The appearance of SO(8) in Costello et al (see #1) could be something octonionic.

i saw this
[Submitted on 25 Aug 2022]

Why do elementary particles have such strange mass ratios? -- The role of quantum gravity at low energies​


Tejinder P. Singh

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infrared. Using the octonions as space-time coordinates, we construct a pre-spacetime, pre-quantum Lagrangian dynamics. We show that the symmetries of this non-commutative space unify the standard model of particle physics with SU(2)R chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge, and leads to a theoretical derivation of the mysterious mass ratios of quarks and the charged leptons. Quantum gravity is quantisation not only of the gravitational field, but also of the point structure of space-time.


Comments:34 pages, 6 figures, pedagogical article, invited contribution for special issue `New advances in quantum geometry', Eds. Shidong Liang, Tiberiu Harko, Matthew J. Lake
Subjects: General Physics (physics.gen-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)
Cite as:arXiv:2209.03205 [physics.gen-ph]
(or arXiv:2209.03205v1 [physics.gen-ph] for this version)
 
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Two new papers on celestial holography:

Asymptotic Symmetry algebra of N=8 Supergravity

Might be something octonionic. Also, at the end the authors say it builds on Hawking et al (2016), on the asymptotic "soft hair" of black holes.

A discrete basis for celestial holography

The title refers to wavefunctions at infinity (on the celestial sphere), which are holographically dual to events within space-time. The paper contains a new jargon word, "news", e.g. it refers to news functions, news signals, decay rate of the news. I assume it has something to do with causally propagating information.
 
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Buried in a new twistor paper

Massive ambitwistor-strings; twistorial models

is some more about SO(8) and triality as it relates to twistors:

In six dimensions, twistors are pure spinors of the conformal group SO(8, C). This group has three eight-dimensional representations: two spinorial ones with opposite chirality and the vector. Triality (most naively seen as the 3-fold symmetry of the Dynkin diagram of SO(8, C)) permutes these three representations into each other

There are descent relations connecting 6d twistors to 4d twistors, which I suspect are parallel to the reduction of an M5 brane to a D3 brane.
 
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kodama said:
does this impact Woit project ?

or 3 generation from octonions?
As Penrose recounts, twistors have a handedness to them, which can be used to model the difference between positive and negative frequency, or the difference between positive and negative helicity (helicity being, roughly speaking, the value of a particle's spin). There are also duals of ordinary twistors, e.g. Andrew Hodges's momentum twistors.

Then, one can try to have a twistor which in some way overcomes this handedness or duality. The best known approach to this is an "ambitwistor". Penrose touts these bi-twistors as another way to do that. They consist of two twistor variables. He's interested in using them for twistor gravity.

In my analysis of Woit's project, I found that he also seemed to be counting on a two-twistor combination (e.g. "a twistor-valued field on twistor space?"). But I can't tell the implications yet.
 
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Regarding (3), Woit does mention a potential octonionic generalization in his talk, see slide 31.

could Penrose use of octonions also explain 3 generations as theorized by other papers as discussed before?
 

1. What are twistors?

Twistors are mathematical objects that were first introduced by physicist Roger Penrose in the 1960s. They are a way of describing the geometry of spacetime in terms of complex numbers.

2. How are twistors related to celestial holography?

Twistors are closely related to the theory of celestial holography, which is a proposed way of understanding the structure of the universe. According to this theory, our 3-dimensional universe may be projected from a 2-dimensional surface at the edge of the universe, much like a hologram.

3. What is the significance of twistors in modern physics?

Twistors have been used in various areas of modern physics, including quantum field theory and string theory. They have also been used in the study of black holes and the holographic principle, which suggests that information about the universe is encoded on its boundary.

4. Can twistors be observed or measured?

No, twistors are purely mathematical objects and cannot be observed or measured directly. However, they have been used to make predictions and calculations in physics that have been confirmed through experiments and observations.

5. Are there any practical applications of twistors?

While twistors have not yet been applied in any practical technologies, they have been used in theoretical physics to better understand the fundamental nature of the universe. They may also have potential applications in quantum computing and information theory.

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