Three papers as the tip of an iceberg

[mitchell porter]

I want to make a self-indulgent post about three papers that came out on the arxiv today. It's self-indulgent because there's no obvious logical connection between the three papers, but I want to muse aloud about their meaning and see what I can find.

The three papers are http://arxiv.org/abs/1105.5632" , author of the fuzzball model of black hole microstates. As I will explain, although the papers are on three different topics, the first two do have a potential connection, by way of twistor string theory. Mathur's doesn't fit that template, so for now I'll just consider it a reminder that string theory still doesn't have a completely transparent model of black hole microstates, and we'll see if, by the end, it naturally reenters the discussion.

Let's start with Maldacena's paper. In my mind, Maldacena has taken Witten's place as the leader in theoretical physics. The idea that theoretical physics has a leader is itself dubious, but here's the pragmatic meaning I associate with the title: There was a time when the simplest way to keep track of theoretical advances was just to read Witten's papers. Even if Witten didn't originate something, any important development would still show up in his papers, described lucidly and insightfully. But now, if I had to specify one person to read, it would be Maldacena. Maldacena's corpus and Witten's corpus are quite different; for example, Maldacena's papers are mostly about AdS/CFT. But I think this reflects the evolving state of theoretical physics. I'd say that when Witten entered the field, the theoretical kingpin was Gerard 't Hooft, for the role he played in making the standard model viable. Then Witten was the dominant figure during the long period of speculative theoretical development which took us from the standard model to M-theory. And now Maldacena's big discovery dominates the agenda in the era of M-theory.

So I am naturally disposed to treat a Maldacena paper as a big event, or at least as worthy of intensive study, for clues regarding where we are and where we're headed in theoretical physics. What does this new paper contain? By my reckoning, there's a clarifying technical advance, an intimation of expected future progress, and something big that I don't understand.

The clarifying technical advance is the observation that "conformal gravity", with the boundary condition "no ghosts in the future", reduces to "Einstein gravity". It's somewhat alarming to see how many different theories of gravity exist in the literature, so it's useful to be told that two of them are this tightly connected, it reduces the chaos a little.

The intimation of expected future progress is: everything in the paper that concerns gravity in de Sitter space. One consequence of AdS/CFT is that it has made quantum gravity in anti de Sitter space, if not a solved problem, a problem in which progress is largely a matter of making an effort. But de Sitter space is both an unsolved problem and far more relevant to the real world, at least cosmologically. This paper, however, contains a number of new results, building on http://arxiv.org/abs/astro-ph/0210603" from 2002. This encourages me to think that quantum gravity in de Sitter space will one day be as "solved" as AdS now is: there will be a consensus on how to think about it, and a consistent body of results and techniques to apply.

Something big that I don't understand: this is part 6 of the paper. That one type of gravity (conformal) should reduce to another (Einstein) in the same dimension, it's interesting but it's easy to understand, no more challenging conceptually than a change of variables. But to be told that 4-dimensional conformal gravity describes something about gravity in 5-dimensional de Sitter space - it's confusing, it sounds important, it even sounds important because it's confusing. I definitely know that I don't understand what's at work here, and so the payoff for actually getting to the bottom of it is unknown.

One reason it's confusing is that, if you're used to AdS/CFT, you're used to gravity in one dimension being related to a non-gravitational theory in a lower dimension. That this is a gravity-gravity relationship is mystifyingly novel.

Now here I want to mention a few other curious assertions I've seen in the literature, which I think are clues as to what's going on here. That is, in trying to understand the bigger picture, I would be revisiting these other papers for guidance. The first comes from that 2002 paper by Maldacena, which is also about the relationship between dS and AdS. In section 5, he mentions a difference in how dS/CFT works for dS4 and dS5: "the nonlocal piece in the wavefunction which determines the stress tensor seems unrelated to the local piece which determines the expectation value of the fluctuations. In other words, dS5/CFT4 would tell us how to compute the non-local piece in the wavefunction but will give us no information on the local piece." There's a special property here, of gravity in 5-dimensional de Sitter space, which I just bet is related to this new oddity whereby there's also a connection to 4-dimensional conformal gravity.

My next two clues bring us to Simon Caron-Huot's paper, which is part of the big attempt to completely solve N=4 super-Yang-Mills. This is the field theory which figured in the original AdS/CFT duality, but AdS space isn't playing much of a role in his discussion. Nonetheless, let me mention my "clues". First, a handful of recent papers using the Goncharov symbol technique to compute correlation functions in 6-dimensional Yang-Mills theory - see citations 52 to 55 in Caron-Huot. These six-dimensional quantities apparently have very immediate relationships to the four-dimensional theory.

My other clue was something I found in http://arxiv.org/abs/alg-geom/9601021" . Start with section 1.1. Here I summarize something I don't really understand, but I'll state the gist as I see it: Hyperbolic spaces are highly rigid, their volumes are transcendental numbers obtained from polylogarithms, and the odd-dimensional case is far more complex and interesting than the even-dimensional case. In odd dimensions, the rigidity implies strong and nontrivial constraints on how a hyperbolic space can be chopped up and reassembled, and these constraints in fact define an algebra which is a "motivic cohomology".

Referring to my earlier post about https://www.physicsforums.com/showthread.php?t=490749", I'll point out two things: formulae in N=4 Yang-Mills which evaluate to combinations of polylogarithms, and formulae which evaluate to a surface area in anti de Sitter space. I believe that these pure-math observations by Goncharov must lie at the root of this conjunction. AdS space emerges as the space of energy scales for a field theory (the domain of RG flow, for a non-conformal theory), certain amplitudes are given by volumes in AdS space, and volumes in AdS space are polylogarithms featuring in a combinatorial motivic algebra. It's obvious that it must all cohere somehow, but the details escape me, and it sounds like even the experts haven't got it straight yet.

But if we can return to this phenomenon of crossovers between 4, 5 and 6 dimensions, occurring in Maldacena's paper, Caron-Huot's paper, and the recent papers employing the Goncharov symbol technique, it seems likely that the "crossover phenomenon" is also related to the "motivic synthesis". Also, I should mention that N=4 Yang-Mills is the worldvolume theory of a stack of D3-branes, and D3-branes are actually M5-branes with two dimensions compactified, and there is a big body of work (by Gaiotto and others) on the 4-dimensional theories resulting from the compactification of the 6-dimensional worldvolume theory of M5-branes. (Another reminder: this theory is dual to M-theory on AdS7 x S4.) There are papers by Witten in which this 6d to 4d reduction is associated to the Langlands program. There is a paper by Weinberg, cited by Caron-Huot, in which a 6d formalism is developed for employment in 4 dimensions. The more of these facts that I list, the more obvious it becomes that there is an enormous coherent synthesis to be unearthed here, much of which would already be evident to these authors. The challenge for outsiders is to crack enough of the code to understand what is already being said and, more importantly, being presupposed, in these papers written by one expert for their colleagues.

I think all of that is what I really needed to say. I've been seeing these connections build and build and build without knowing how to organize them. I still don't, but, at least the problem is now in the open! The challenge is to find the important clarifying insights which will organize this mess of data and discoveries, and allow one to see the essence of what is at work here.

I'll return to the actual content of Caron-Huot's paper later on, I think. And I haven't forgotten Mathur. I want his work to stand as a reminder that a lot of the stringy discussion of black holes (in AdS spaces and elsewhere) is still very heuristic in nature. But the microscopic description of black holes in AdS space is one of the things which, in time, AdS/CFT ought to provide us with. And in turn that should tell us how black holes work in dS/CFT, and thus in the real world. In the application of AdS/CFT to quark-gluon plasmas, one uses a duality between thermal states in a field theory and black holes in AdS space, and so I wonder if all black holes in every dimension can ultimately be understood as a sort of deconfined Yang-Mills plasma. Another aspect of the N=4 revolution is the understanding of gravitational amplitudes as squares of Yang-Mills amplitudes; it goes back to the fact that in string theory, you can understand a closed string (graviton) as two open strings (gauge bosons) joined together. http://arxiv.org/abs/1105.2565" was a recent big advance in the sub-sub-field of "relationships between Yang-Mills theory and perturbative gravity". But that really does exhaust my ability to tie this stuff together, for now.

... OK, I see I forgot to mention how twistor string theory fits in. Twistor string theory was where the N=4 revolution got underway: it was the first recent use of twistors to simplify super-Yang-Mills theory. But this original formulation was considered slightly pathological, because it consisted of Yang-Mills coupled to conformal gravity, and conformal gravity is nonunitary. So if Maldacena has discovered how to fix conformal gravity, by imposing these future boundary conditions, then he may also have fixed twistor string theory.

 

[Haelfix]

There have been a number of truly excellent theory (and phenomenology) papers in the past couple weeks on arxiv. I really liked the Maloney paper a few days ago: arXiv:1105.4733.

 

[Physics Monkey]

I hate to pick at this fledgling thread, but Maldacena is certainly not the leader of theoretical physics. This is just silly given how much of theoretical physics lies outside of quantum gravity.

I suspect what you mean by theoretical physics is roughly advanced quantum field theory and string theory, and here I would agree he is a leader (among many) in the sense that most people listen carefully to him and even worship him.

 

[erkokite]

Another paper that might be somewhat relevant:
http://arxiv.org/abs/1104.4543"

The bottom paragraph on page 14 is particularly relevant.

And yet another on N=4 Twistor Yang Mills:
http://arxiv.org/abs/1104.2605"

 

[atyy]

Regarding dS/CFT, it's commonly said we don't know how to do quantum gravity in such a space since the gauge-invariant observables would be accessible only to people outside the universe. (Is this related to this thing I've read in introductory string texts that because of general covariance one has to go the S-matrix directly, and only on-shell quantities make sense?)
Witten http://arxiv.org/abs/hep-th/0106109

Another strand of thinking has been to use relational observables or partial observables or something like that. It goes back to before Rovelli, but just listing recent papers:
Rovelli http://arxiv.org/abs/gr-qc/0110035
Giddings, Marolf, Hartle http://arxiv.org/abs/hep-th/0512200

Is there a problem? Do Rovelli's and Giddings et al's sort of proposals point to a solution?

 

[marcus]

I really liked the Maloney paper a few days ago: arXiv:1105.4733.

Alex Maloney is the friend of a friend! I'm told to expect great things of him. Seems to have a strong focus on gravity in 3D, 4D, 5D, or thereabouts. Has worked with Strominger and with Witten. McGill made a good move when they brought him there, I expect. I'm glad you mentioned his paper:
http://arxiv.org/abs/1105.4733

===================

Mitchell, I understand what you mean about a convenient figure to watch, and the progression you mentioned:
't Hooft --> Witten --> Maldacena
It helps to have bellwethers who show where a field is going. They integrate the trends and make an observer's life easy. (As well as sometimes creating and leading major developments.)
I added Maldacena's recent paper to the non-string QG bibliography yesterday as possibly of use in QG research even though not explicitly about quantum gravity.
Just to have it in front of us, I'll paste the abstract:
http://arxiv.org/abs/1105.5632
Einstein Gravity from Conformal Gravity
Juan Maldacena
(Submitted on 27 May 2011)
"We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean anti-de Sitter spacetimes. This simple Neumann boundary condition selects the Einstein solution out of the more numerous solutions of conformal gravity. It thus removes the ghosts of conformal gravity from this computation.
In the case of a five dimensional pure gravity theory with a positive cosmological constant we show that the late time superhorizon tree level probability measure, |Psi[g]|², for its four dimensional spatial slices is given by the action of Euclidean four dimensional conformal gravity."

 

[unusualname]

Maldacena is not the leader of theoretical physics, he is like Andrew Wiles, he obtained a proof of an abstract mathematical construction, and that is impressive no doubt.

Physics is in a stage of "bollocks" at the moment whereby any genius may post their latest "discoveries"/"analysis" on arXiv.

Witten is too old (sorry) for original contributions. Everyone needs a real spike in the rear to progress.

.

 

[MTd2]

Isn't that conformal gravity what Penrose proposed to recycle the universe?

 

[marcus]

Physics is in a stage of "bollocks" at the moment whereby any genius may post their latest "discoveries"/"analysis" on arXiv.
...

Well for goodness sake! We're all just trying to be helpful.

 

[mitchell porter]

erkokite #4, MTd2 #8, I've had no time to understand Penrose's cyclic conformal cosmology or 't Hooft's latest ideas. But I have noticed one thing: 't Hooft is also proposing a peculiar derangement of the usual idea of scale, just as occurs at the end of an "aeon" in Penrose's new cosmology. See the synopsis at the end of this http://www.technologyreview.com/blog/arxiv/24143/" . In his paper, 't Hooft adds that, since the holographic principle (in one incarnation) relates spacetime area to number of bits of information, perhaps the quantity of information flow through a region sets its physical scale.

 

[mitchell porter]

I should also mention Paul Frampton, who wrote papers on both http://arxiv.org/abs/0706.4259" . The conformality paper is ideologically interesting in that it describes at some length an alternative philosophy for high-energy physics, in which one looks for the appearance of exact conformal symmetry, rather than exact supersymmetry, at higher energies. (But see the "Note Added" on page 160.)

 

[tom.stoer]

Witten's no-go arguments against QG in dS seem to be rather vulnerable to disproof (just as many other no-go theorems) b/c they rely heavily on smooth spacetime geometry and things like that; what about theories where spacetime disappears completely and re-emerges from a more fundamental algebraic structure (LQG, matrix theory, ...)?

 

[atyy]

Witten's no-go arguments against QG in dS seem to be rather vulnerable to disproof (just as many other no-go theorems) b/c they rely heavily on smooth spacetime geometry and things like that; what about theories where spacetime disappears completely and re-emerges from a more fundamental algebraic structure (LQG, matrix theory, ...)?

Witten's questions remain in emergent spacetimes. His problem is how do you construct "local" observables that someone in the spacetime can use? There's a similar problem in AdS/CFT, since at present the observables are those for a boundary observer. Maybe understanding that case will point to a solution for other spacetimes, especially since there seem to be ideas for http://arxiv.org/abs/1005.5403" .

 

[tom.stoer]

I do not agree.

Look at the surface of an infinite lake. The observable "position of water" is nonsense, but the observable "position of an atom" remains valid. But w/o referring to microscopic degrees of fredom you can't construct these "microscopic" observables.

With smooth background spacetime you can only construct observables "on top of this spacetime"; so perhaps you eliminated (or omitted from the very beginning) what you are looking for.

 

[atyy]

I do not agree.

Look at the surface of an infinite lake. The observable "momentum of water" is nonsense, but the observal "momentum of an atom" remains valid. But w/o referring to microscopic degrees of fredom you can't construct these "microscopic" observables.

With smooth background spacetime you can only construct observables "on top of this spacetime"; so perhaps you eliminated (or omitted from the very beginning) what you are looking for.

I don't think this is different from what I said. AdS/CFT is a case of emergent spacetime, like what you are talking about. The question is can one demonstrate a concrete construction? That's what the Kabat et al and Gary et al papers attempt.

Is this an analogous problem: The position of a non-relativistic atom is observable. But there is no relativistic position operator. How does the non-relativistic position operator emerge?

 

[atyy]

The intimation of expected future progress is: everything in the paper that concerns gravity in de Sitter space. One consequence of AdS/CFT is that it has made quantum gravity in anti de Sitter space, if not a solved problem, a problem in which progress is largely a matter of making an effort. But de Sitter space is both an unsolved problem and far more relevant to the real world, at least cosmologically. This paper, however, contains a number of new results, building on http://arxiv.org/abs/astro-ph/0210603" from 2002. This encourages me to think that quantum gravity in de Sitter space will one day be as "solved" as AdS now is: there will be a consensus on how to think about it, and a consistent body of results and techniques to apply.

Something big that I don't understand: this is part 6 of the paper. That one type of gravity (conformal) should reduce to another (Einstein) in the same dimension, it's interesting but it's easy to understand, no more challenging conceptually than a change of variables. But to be told that 4-dimensional conformal gravity describes something about gravity in 5-dimensional de Sitter space - it's confusing, it sounds important, it even sounds important because it's confusing. I definitely know that I don't understand what's at work here, and so the payoff for actually getting to the bottom of it is unknown.

This new paper by http://arxiv.org/abs/1106.1175" , which, naively read, indicates that the dual theory for dS is a theory of gravity. However, that depended on the absence of boundary conditions at future infinity. The new paper suggests that boundary conditions can be imposed that make it more like AdS, so that the dual will be a CFT without gravity.

 

[tom.stoer]

But there is no relativistic position operator.

Why not?

 

[atyy]

Why not?

The physics reason is that if you try to localize a particle with greater and greater precision, you will create more particles.

The formal reason is that the position states that come from Fourier transforming momentum states in a Lorentz covariant way are not orthogonal. So a state that is "here" is also "there". There are Newton-Wigner position states that do represent position, but only in one frame. In another frame, they are nonlocal.

I read this in Paul Teller's http://books.google.com/books?id=4f3S6DJ8OZIC&source=gbs_navlinks_s , p86-89.

 

[tom.stoer]

Hm, what about "x" as a position operator? where does this naive contruction fail?

 

[atyy]

Hm, what about "x" as a position operator? where does this naive contruction fail?

I don't know how to form the position operator in quantum field theory. The operator has to be defined by some sort of commutation relation, or by its action on some basis states. For example, if I start from Eq 2.6 of http://staff.science.uva.nl/~jsmit/qft07.pdf or Eq. 2.20 of http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf , how do I make an operator x?

I think it might be ok in relativistic quantum mechanics, but am not sure, and relativistic QM itself has problems as a "fundamental" theory.

 

[negru]

Conformal gravity is definitely a big thing and connecting these three papers was quite inspired!

I'll have to read the paper carefully to see how everything works out, but if conformal gravity can be made ghost free it's huge news for the twistor and grassmannian stuff. One of the biggest problems with extending the twistor developments to gravity is making sense of the "infinity twistors" which break conformal invariance. They don't appear in YM amplitudes, but they do in gravity ones. There are also some completely unrelated papers (can't find them now) which claim to obtain einstein gravity from conformal gravity by - surprise - introducing infinity twistors. The grassmannian also spits out conformally invariant objects, so getting conformal gravity from it first might be the way to go.

(I don't see Mansfield cited in the paper btw, he was of course big on this topic, probably from the wrong perspective though)

In any case this paper changes many things!

 

[negru]

oops of course i meant mannheim not mansfield and he is indeed cited

 

[mitchell porter]

Regarding Smilga vs Mannheim (footnote 1 in Maldacena) on whether ghosts in higher-derivative theories are fatal, http://arxiv.org/abs/1012.5202" observes: "this catastrophic behaviour has been explicitly exhibited on toy models only... By the same token, most proposals to tame ghosts have been also illustrated by toy models only".

I now notice that Maldacena's paper says he can get Einstein gravity in de Sitter space from conformal gravity with a boundary condition. Which is still important, and perhaps even phenomenologically relevant, but not as universal a result as one might infer from the title. :-)

The switching between Minkowski, de Sitter, Euclidean anti de Sitter, and between 4 and 5 dimensions, is still too much for me to sort out. But getting the measure for Einstein gravity in d=5 dS from the action for Euclidean d=4 conformal gravity (section 6) puts me in mind once again of the https://www.physicsforums.com/showthread.php?t=506476", since it has a holographic flavor to it.

I didn't yet manage to say enough about Caron-Huot's paper, which naively appears to contain several significant features. First, it begins to explain the https://www.physicsforums.com/showthread.php?t=490749" obtained using Goncharov symbols. Second, he does a funky thing (page 15) in order to maintain conformal invariance: while otherwise working in four dimensions, he takes a shortcut through AdS space in order to have a path connecting two points which are otherwise not null-separated. This is possible because he's using Weinberg's 6-dimensional notation. But at the same time, he's working with twistors, which I thought were only a phenomenon of the boundary theory, so (note to self) there's an apparent contradiction to be resolved here.

In case anyone ever lands on this thread looking for commentary on Mathur's GRF essay, here's a http://freelance-quantum-gravity.blogspot.com/2011/05/great-day-in-arxiv.html" .

Finally - negru, I'm sure you noticed http://arxiv.org/abs/1106.1558" last week, a step towards obtaining Vasiliev gravity from string theory?

 

[negru]

Yup I did, I have to say I wasn't expecting the HS theory to come from the beta function of a sigma model..in any case this makes understanding AdS4/CFT3 even more important than before. In particular, could the bilocal field approach that constructs AdS from the CFT teach us anything new about string theory?

If this works out to all spins AdS4/CFT3 could become the new AdS5/CFT4

 

[mitchell porter]

Several superficial observations:

http://arxiv.org/abs/1102.2910" is the most recent in a series of papers on constructing local bulk observables from CFT operators. The approach employed for free fields in earlier papers breaks down (spacelike operators don't commute) for interacting fields, but in section 4 (especially 4.4) they restore spacelike commutativity with a bilocal correction term. I emphasize that this is about constructing local bulk observables, which is more or less the same thing as constructing a local AdS geometry.

I've just noticed that Polyakov's vertex operators are generating frame fields for Macdowell-Mansouri gravity! That's a gauge theory of gravity, of https://www.physicsforums.com/showthread.php?t=506509#5" of the loop-vs-string difference. I must still be missing something...

Progress for AdS4/CFT3 is also potentially relevant phenomenologically, if one can generate a hierarchy of dimensions as in Polchinski and Silverstein's "gardening the landscape" paper.

By the way, thanks for your remarks about the infinity twistor, that was educational. Were Abou-Zeid et al (another approach to the twistor string) the people trying to employ it in conformal gravity?

 

[negru]

I was thinking about http://arxiv.org/abs/gr-qc/9907067, see top of page 4

Unfortunately because everyone thought conformal gravity is simply garbage I couldn't get any expert comments on this paper and its possible relevance to the grassmannian and stuff. Maybe things will be different now.(i did mention the paper in my thesis so that's a start :P )

 

[mitchell porter]

There are two recent papers which can be read as sequels to Maldacena on conformal gravity and Caron-Huot on the N=4 super Wilson loop.

First, http://arxiv.org/abs/1108.2227" by Andrew Hodges. This is an extension of BCFW recursion to gravitons. It's actually huge news for twistor people. All the big twistor progress has been for N=4 Yang-Mills. Arkani-Hamed and pals have had their eye on N=8 gravity, but there hasn't been a starting point. Now there is, and as negru surmised, it involves the infinity twistor. Hodges also suggests that his formulae should have an interpretation in terms of the (hitherto problematic) closed sector of the twistor string.

Second, http://arxiv.org/abs/1108.1575" by Sever, Vieira, and Wang. This is directly a follow-up to Caron-Huot, and like his paper, it's another technical advance for N=4 Yang-Mills.

Both these papers cite http://pirsa.org/index.php?p=speaker&name=Jacob_Bourjaily".

Today there's a third paper, http://arxiv.org/abs/1108.2381" , which provides some context for Hodges's discussion of the relation between N=4 gauge theory and N=8 gravity. The standard idea (KLT relation) is that graviton scattering consists of two copies of gauge boson scattering attached together (and this paper proposes to do this in the form of two Alday-Maldacena minimal surfaces in AdS space).

 

[negru]

You know I'm becoming more and more convinced that it's conformal gravity that we need to understand in terms of grassmannians. I mean, it makes sense. You have conformal symmetry which the grassmannian likes, you have the connection to the twistor string (remember how conformal gravity automatically appears there - it's directly tied to Yang-Mills amplitudes). This (generalized) grassmannian might be some equivalent expression for the (full) twistor string. Which in appropriate limits or whatever can give either YM or gravity amplitudes. Then breaking the conformal symmetry to get normal gravity should be doable, as per some of the above papers. Now, if this is true, it might be sad in the sense that such constructions would be unique to YM and gravity (not that YM and gravity aren't the most important qft's, but the hope was to completely generalize this formalism).

Now it's strange that non-conformal gravity is already so similar to YM (klt, bcj, link representation). So i dunno. Time to find some explicit computations of scattering amplitudes in conformal gravity...anyone know any good references?

 

[negru]

hm. that was dumb. what's an s-matrix for a non-unitary theory?

 

[atyy]

How about a pseudo-unitary theory - I remember reading this mysterious statement that time evolution is still unitary in the dS/CFT thing that mitchell porter posted about.

 

[mitchell porter]

http://arxiv.org/abs/0811.1341"

 

[Chronos]

It still looks like turtles all the way down to me.

 

[negru]

Yeah I don't know about the unitarity thing. It really annoys me that it's not explored more. Conformal gravity seems like a potentially very useful theory. I don't know if solving its problems is just hard, likely impossible, shown to be impossible, or what? For example, why do witten and berkovits write a whole paper about conformal gravity ( http://arxiv.org/abs/hep-th/0406051 ) and say:

This simple observation suggests that four-dimensional conformal supergravity theories
might be relevant to the real world – perhaps with the aid of some mechanism of
spontaneous breaking of conformal invariance. However, they in fact are generally considered
to be an unsuitable starting point for describing nature, because they lead to fourth
order differential equations for the fluctuations of the metric, and thus to a lack of unitarity.
We have no reason to question these beliefs and we will later describe some facts that
illustrate them.

Really, no reason to question these beliefs? Then why write a paper about something that doesn't make any sense...this is just beyond me..I mean, this ghost stuff in CG is just in perturbation theory (as far as I know). Non-perturbatively it might be ok. It just sounds silly to me to disregard the theory so easily

 

[negru]

Mitchell, that is in fact the only paper I knew. Is there really nothing more comprehensive out there? I'm particularly interested whether there's anything like the KLT relations in conformal gravity. Very interestingly, eq 4.14 shows that the 4 point ConformalG amplitude is proportional to the EinsteinG amplitude. I wonder if this holds for higher points?

And more generally, given the supposed non-unitarity of CG, does its S-matrix make any sense? Non-unitarity means probabilities not adding up to 1 due to ghosts, right? How about just tree level?

 

[mitchell porter]

Really, no reason to question these beliefs? Then why write a paper about something that doesn't make any sense...this is just beyond me..

It's the equivalent for theory of OPERA's FTL neutrino paper. They "know" it doesn't make sense, but it's "there" (in the twistor string), so they tell the world what they found and maybe the world will explain it for them.

I'm particularly interested whether there's anything like the KLT relations in conformal gravity.

Maybe yes - http://arxiv.org/abs/1108.3085" .