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Classic Literature in Quantum Gravity?

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I've seen it said in various places that a major reason people like string theory as a theory of quantum gravity is that it does a good job of matching our prejudices about how a quantum gravity theory ought to behave. For example, the area law for black holes has been demonstrated for some black holes, and the lack of an off-shell formalism seems to be related to the non-existence of any observable aside from the S-matrix.

I'm wondering:

  1. What are these prejudices?
  2. Where do they come from?
  3. In particular, which by-now-classic papers/books/reviews should I be reading if I want to learn more about them?

Note that I'm not looking for papers on string theory or whatever. I'm trying to understand what a generic high energy theorist might have thought about gravity circa-1983.

For the sake of this question, let's suppose that I have a PhD in theoretical physics, but focused mainly on computing structure functions, and that my knowledge of GR is essentially limited to what's in Wald.

[A Late Addendum: It's become clear that I didn't ask my question clearly. I've been lucky and gotten some excellent answers anyways. But-- just for the record -- what'd I'd been wondering is this: Which bits of the historical literature led us to our picture of how a 'generic' quantum gravity theory ought to behave? (This is the reason I brought up string theory in the original question. I have no desire to discuss its relative merits here. I only mentioned it because its relative popularity indicates that there are some criteria we think a theory of quantum gravity ought to satisfy.)

This is obviously a tricky question to answer, for several reasons: 1) there might not be such a thing as a generic quantum gravity theory, 2) more recent developments in theoretical physics have shaped our perspective on what's important, and 3) people writing early papers on the subject didn't necessarily know what was important.]

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asked Oct 25, 2011 in Theoretical Physics by user388027 (415 points) [ no revision ]
retagged Mar 18, 2014 by dimension10
This probably should be community wiki...

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Personally, I am not so crazy about catch-all questions. There could be hundreds of good answers to this question, each with different flavours depending on the required level and background of the OP. Maybe there is a way to make the question more narrow and specific?

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I've added a little context. The question may still be too broad to satisfy.

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Alright, CW it is. Hope for some interesting answers.

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Quantum gravity was not proven to be perturbatively non-renormalizable until 1985 (http://dx.doi.org/10.1016/0370-2693(85)91470-4) So, I'd guess you want to revise your date to circa-1986 to obtain a clearer picture of what "a generic high energy theorist might have thought"

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"my knowledge of GR is essentially limited to what's in Wald." Modulo the fact that Wald was written after 1983, this could very well apply to most high-energy physicists at the time :)

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5 Answers

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I will try to answer the narrowest reading of this question: what expectations do we have of quantum gravity based on general principles, perhaps combined with semi-classical reasoning and other clues (regardless of history, which I’m not qualified to comment on). I'm not going to discuss in detail how this distinguishes string theory from other approaches to quantum gravity. Let me just express my personal opinion, which is that following only what we know with great confidence to be true, some of which is specified below, inevitably leads to string theory or something very much like it.

Also, since this is such a general question and an appropriate answer can be very long, I'll just write a short list off the top of my head for now and wait for things to focus a bit. I can edit my answer later as needed (if I have the time). For the same reason, and since looking for references is time consuming, please let me know which of these points you'd want to look into, and I'll add references as needed. I’m also not sure if your question is mainly historical, or is defined more by the content (which is the way I treated it, namely: what do we know of QG independent of specific approach) so correspondingly I am not sure which references you want.

Lorentz Invariance:

It is nearly impossible to break Lorentz invariance at short distances without getting large number of huge violations of any test of LI at observable energies. It is nearly impossible to write a consistent quantum theory with small violations of LI. Therefore, any theory of short distance physics has to be exactly LI. Luckily, this is a very stringent constraint, this by itself eliminates most of the approaches to QG out there, or many things you'd want to try if you didn't know better.

Non-Renormalizable theories are "effective":

GR is non-renormalizable when quantized around flat space (or any other smooth background). Though some miracles may sometime happen, by and large non-renormalizable theories indicate that the degrees of freedom and action you use at low energies are not "fundamental", they are effective description of short distance physics which may be radically different. To steal a slogan from Ted Jacobson (who used it in a different context), you don't quantize the metric for the same reason you don't quantize ocean waves.

Gauge "symmetries" are redundancies:

This is a more modern line of reasoning, it goes to what precisely in meant by the expression "quantum gravity." For many older approaches diffeomorhpism invariance is the defining feature, for example they will tell you that an operator algebra representing the diffeomorphism group defines a quantum gravity theory. In more modern approach gauge symmetry is more of a technical tool -- there can be many definitions of the same quantum theory utilizing different sets of gauge redundancies, and each such gauge redundancy is part of the language most appropriate for a specific classical limit of the theory. Defining QG by what redundancies it possesses seems besides the point - QG should be defined rather as any quantum theory which reduces to classical general relativity at long distance scales.

Background Independence and the problem of time:

Quantum theory needs some structures, for example a non-dynamical time, for its formulation. That can be done when fixing a background spacetime, but if you want spacetime to be fully dynamical, no such structure can be treated as fixed, and you are stuck. Holographic approaches to quantum gravity (like matrix theory or ads/cft) sidestep this issue by using auxiliary variables to define a background-independent quantum gravity theory. The key point that the structures defining the quantum theory are not identified as part of the resulting dynamical spacetime.

Holography vs. locality:

Following from black hole quantum mechanics, and from the fact that there are no local observables in the theory, it is clear that the maximal entropy you can fit in a spatial region scales like the surface area of that region, and not like the bulk volume. Any approach that quantizes a local field will get an entropy scaling like the volume; most of these degrees of freedom are unphysical -- they correspond to local excitations that pack lots of energy in small volume and therefore should correspond instead to black hole microstates. Any approach that insists on strict locality in the quantum theory will treat almost all excitations of the system in the wrong way.

This is also related to the non-existence of off-shell formulation you mention — the theory cannot be probed locally for very physical reasons. Any attempt to calculate these unphysical quantities (say, off-shell Green’s functions which are the basic observables in a local QFT) is bound to get you very confused.

Unitarity in black hole evaporation:

More recent and more tentative line of reasoning, which I am including only because it is so beautiful. This is a line of reasoning that leads to string theory, or something very much like it, as the only way to fully resolve (sometime in the future) the black hole information paradox. Look for one of the latest reviews by Samir Mathur on "fuzzballs" to see this very elegant line of reasoning.

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answered Oct 25, 2011 by Moshe (2,375 points) [ no revision ]
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Let me ask you this Moshe: are you really qualified to speak about, say, what LQG/spin-foams have to say on these topics? If you are, fine. But otherwise, I'd like to see some higher standards of intellectual rigour on TP.SE. Again, what I said to Lubos: we're all physicists here --- let's focus on the physics and leave the spitting at the door.

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After briefly expressing my personal opinion, clearly labeled as such, and which everyone is invited to distegard, I see only one parenthetical reference to any specific approach to QG. Everything else represents model-independent constraints on any approach to QG. Of course, some of these criteria don't reflect too well on some approaches (including for example, closed string field theory), but I was careful not to get into this kind of food fight. Since we are all physicists here, let me also say that the "argument from civility" is equally a distraction from a substantive discussion.

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To respond directly to your question: LQG and the spin foam variant are attempts to canonically quantize gravity, using the Ashtekar variables as the fundamental degree of freedom. Certainly one of the "prejudices" the OP refers to is that directly quantizing Einstein gravity as a QFT (in whichever variables) is both hopeless and misguided, and that a quantum mechanical theory in which you don't have to do that, but still get gravity as part of the story, is a god sent. Pointing out many of the reasons for this attitude is a perfectly rigorous and on-point response to the question.

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perhaps Lubos has made me a bit touchy. My question was simply if you were really up to date on LQG research. For instance, if you think it's about quantization of a classical theory then I'm afraid your knowledge is simply out of date. So again: are you a researcher in LQG? Otherwise I don't see how you can stand amongst fellow physicists and claim any authority? This is not physics.SE, where a large majority are laymen. That is the root of my discontent.

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I truly don't see any part of my answer which even refers to LQG directly (not even indirectly, if you don't think of it as quantization of a classical theory), so I am puzzled by your comments. Besides that, I am also not precisely sure what the OP was asking about, and for what purpose. So for all these reasons, I am afraid I have lost interest in any further discussion. Maybe the lesson for the future is concentrating more on concrete and technical issues, and not get into unfocused discussions, which to be honest are not all that much fun.

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I thought the OP was asking for quasi heuristic expectations that a theory of QG ought to conform too. Well thats one of them. Here are more: There are no global symmetries in such a theory and there are no local observables. References shouldn't be too hard to track down, especially since most of them are in the relevant textbooks.. Like Wald, Birrel and Davies the original papers by Wheeler etc

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Look at the discussion under arivero answer, seems the OP is more interested in early QG references than the common model-independent lore which support ST (and yes, also indicates other approaches are misguided). Anyhow, thanks for reminding me of these points, perhaps we’ll have another occasion to have this discussion.

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The only full-fledged, genuine quantum theory of gravity we have (and most likely, the only one that is possible for mathematical reasons) is string/M-theory so textbooks of string/M-theory represent the only canonical literature on quantum gravity that you may find as of 2011 and that is ready to be presented pedagogically to students as material they can further work with, see e.g. this list


Things that have been proposed as "alternative theories" can't really compete with string theory when it comes to the degree of rigor, strength of the connections with the previous established physics, and just simple pure internal consistency and the discouraging quality of canonical textbooks on these subjects is one of the simplest ways to see this fact.

In the same way, you can't really find any meaningful pre-1983 textbooks on quantum gravity, either, because this discipline wasn't understood, almost at all. Right before 1983, people working on the most similar kind of physics (except for 5 string theorists) would do research in supergravity which is really just a field theory generalizing Einstein's general relativity, adding extra fermionic fields and a fermionic symmetry (local supersymmetry) but it's a field theory. Most of the calculations they did were classical, just like in classical GR, and the attempted quantum calculations using the tools of quantum field theory were seen to lead to a divergent short-distance behavior. That changed in 1984 when superstring theory was shown to be free of anomalies and UV problems while it was capable of producing all the right classes of physical phenomena known from supergravity and gauge theories coupled to matter.

While the theories – quantum gravity and string theory – almost certainly have to be the same thing, the two names are used differently. "Quantum gravity" is reserved for the research of questions that can only be asked or that only become hard if the physical system respects both the postulates of quantum mechanics as well as those of general relativity (gravity). They're the questions of the type "how do the postulates or effects of quantum mechanics influence one or another situation where the curved geometry plays a key role?".

Some of these questions are answered by string/M-theory in its current state; some of these questions were approximately answered even by QFT tools before string theory; some of these questions remain open.

For example, the Wheeler-DeWitt equation (together with its various solutions such as the Hartle-Hawking state) mostly belongs to the third category (the things not yet established). It's the equation $H\Psi=0$, expressing the idea that the Hamiltonian constraint in GR actually encodes the full evolution in time, something that is possible due to the ambiguous meaning of the word "time" in diffeomorphism-symmetric theories. To solve it, one must first define his own time, by linking it to some coordinate-independent evolving quantity, and so on.

Partial arguments why this equation should be true exist, much like some approximate demonstrations how it could work in truncated schemes. However, at the end, this equation should only be applied to the Hilbert space of a full working theory of gravity. At this moment, and most likely not only at this moment, string/M-theory is the only theory that satisfies this condition. Unfortunately, the understanding of the Wheeler-DeWitt equation, if one exists, at the level of string theory is highly incomplete, to put it euphemistically. In fact, the equation itself is unnatural because the diffeomorphism symmetry is just one among infinitely many similar symmetries and the Hamiltonian linked to it is just one of many operators that should be treated on equal footing if they are treated at all. So it's questionable whether the Wheeler-DeWitt equation will ever tell us something new again or whether it has been superseded. Maybe, it should be replaced by some more complex structure we don't know.

Before 1983, the Wheeler-DeWitt equation was as confusing as today and our knowledge about it boils down to one or a few papers, most of which remain confusing. This has never been a stuff ready to be printed in textbooks and taught to students. It's a speculative suggestive work in progress that doesn't have to lead anywhere.

The Hawking (black hole) radiation is sometimes included into quantum gravity but Hawking's original calculation was done within effective quantum field theory, really ordinary non-gravitating quantum field theory on a curved background. So strictly speaking, it shouldn't really be considered a part of quantum gravity. In this way, he could have derived the black hole temperature. Indirectly via thermodynamics, this also implies that black holes should have an entropy and many microstates. Why they possess the required entropy had been a mystery through the mid 1990s when the entropy was microscopically computed in string theory – for the first black hole and then for dozens of others (lots of multi-parameter supersymmetric black holes, near-supersymmetric i.e. near-extremal black holes, and some completely non-supersymmetric black holes in which the stringy "tricks" may be applied as well). Aside from consistent and convergent formulae for graviton scattering amplitudes, this became a huge piece of new evidence that string theory is a consistent theory of quantum gravity and it remains the only theory that is able to solve either of these problems.

It's not true that all questions surrounding the information loss paradox have been resolved. While we know that the information isn't lost after all, the non-local processes that (as we know indirectly) surely take place in string theory are not well-understood. How far they operate? Why? How much can they change at all? Could they become observable in non-black-hole experiments? And so on. These questions remain mostly open.

A special part of quantum gravity is quantum cosmology. Here, we're not really talking about the common description of inflation that is needed to explain the cosmic microwave background; the latter is, once again, governed by quantum field theory on fixed curved backgrounds and shouldn't really be included in quantum gravity per se. Most of it remains inconclusive within string theory – even though people have already taken their fast interpretations what important processes happen when they talk about the multiverse etc. – and once again, it is not addressed by other approaches at all.

There are some other partial questions of quantum gravity that have been understood such as the changing effective dimensionality or topology of spacetime and so on (those things are allowed, do occur, and sometimes they are under complete calculational control). All these things have mostly been clarified by string theory. If you summarize the successes and failures of string theory as a tool to answer general questions about quantum gravity, the situations (including singularities) that are close enough to static ones (where supersymmetry may be preserved etc.) are well-understood in string theory; the heavily time-dependent situations such as the Schwarzschild singularity or the very initial point of the Big Bang are (mostly) not understood. But let me return to the original questions.

Prejudices vs insights

The word "prejudices" is clearly emotionally loaded. Such emotional labels don't belong to the realms of science that investigate totally plausible – and in fact, given the quantitative evidence, very likely – statements. I think that "insights" would be far more accurate but let's call them "general propositions" to be impartial.

String the

answered Oct 25, 2011 by Luboš Motl (10,178 points) [ no revision ]
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A typical Lubos answer, starting by completely disparaging other lines of research. The meat of the answer is fine, but the social commentary is not. I think physics.SE suffered enough of the pointless rhetoric, so I would like to see TP.SE kept "cleaner" and to a much higher standard. String theory is not the only research line in town, and comments to that effect are bordering on libellous.

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Dear Genneth, string theory *is* the only textbook-ready theory of quantum gravity on the market – now as well as at any point in the history of quantum gravity – and this is pretty much the core of the question that was asked, indeed. Physics.SE has suffered a lot from ignorant people who try to spread their opinion which was one of the reasons why a new server with higher standards, protected against unsubstantiated and unjustifiable comments such as yours, became necessary.

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Lubos, I'm strongly tempted to downvote your response. I was asking for references to the early literature, and -- despite writing some 2000 words -- you didn't mention even one.

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@LubošMotl: your dogmatic view that string theory is the only game is town is (I hope) well-known. But it doesn't hold up to any kind of scrutiny (citebase provides a [lower bound](http://www.citebase.org/search?q=%22loop+quantum+gravity%22+or+%22spinfoam%22+or+%22eprl%22&order=DESC&rank=1001&maxrows=10&submitted=Search)). I don't mind the content, but why have the unnecessary comments about sociology? We are all practising physicists here (I hope) so we can all use our critical thinking to evaluate theories when presented with the work.

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FWIW, this contains lots of ingredients for a good answer. The question is a bit unfocused (which is one reason I find it hard to formulate an answer myself), but in one reading one is asked how string theory improves on older approaches to QG. I think the sharp distinction to other (=older, because all other approaches are in fact older) is that string theory does not treat the metric as a quantum variable, rather it is something that emerges in the classical limit of the theory. Lots of the detail on how that improves the situation are in this answer.

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Actually, I realize that all of us omitted important insights about quantum gravity up to Feynman's discovery of the need for ghosts in GR; this was one of a very small number of "not quite trivial" things in QG before string theory that worked and whose importance was established and survived.

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@lubos, I don't think we disagree. In my mind, the sharpest distinction between all approaches called string theory, and all other approaches, is the attitude towards classical GR. The naive approach is to try to quantize it as field theory, treating the metric (or some alias thereof) as a canonical variable. This gets you into a world of grief, which at this point is unlikely to be resolved if only we just find the right trick...ST tells you this attitude is unnecessary, the only thing you need is get GR in the classical limit, and there are ways to get there without "quantizing geometry".

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Perhaps a good idea of what at least part of the community trying to quantise gravity was up to prior to 1984 can be gleaned from the Supergravity Physics Reports by Peter van Nieuwenhuizen. Some of the excitement about the two-loop finiteness of certain supergravity theories (in 4 dimensions) is still palpable from the report and in particular the question of the finiteness of $N=8$ supergravity is mentioned, a topic which is still very much alive today. Of course, these are really quantum field theories of gravitons (and cousins), but that was at the time at least a valid approach towards a quantum theory of gravity.

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answered Oct 25, 2011 by José Figueroa-O'Farrill (2,135 points) [ no revision ]
Dear José, of course, in the late 1970s and early 1980s, this was the branch of physicists closest to e.g. string theorists today - later absorbed by the string/M-community. However, I wouldn't say that their research was really a part of "quantum gravity". They studied it because they were excited by supersymmetry and wanted to apply it to GR as well. At those times, it only gradually became well-known that quantized GR suffers from the 2-loop non-renormalizable problems which energized the SUGRA research but wasn't really ever the deciding issue. SUGRA folks never studied quantum foam etc.

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Dear Luboš, I agree that perhaps this is not what we now would call 'quantum gravity', but I think that if you had asked them at the time, they really were thinking of quantising gravity by standard QFT techniques. The supergravity crowd were the same people who in the early 1970s were computing one- and two-loop graviton-graviton scattering.

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I agree, @José. Dan Freedman was telling me about those approaches in those time. QFT techniques were simply believed, kind of naively.

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Well, it is good as the OP was asking for the hep-th community, not the gr-qc. But some hints about the later could make a more complete answer.

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Alas, I have no idea what the gr-qc community was up to before 1984 :(

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In 1986 we have "New Variables for Classical and Quantum Gravity" by A. Ashtekar, (Syracuse U. & UC, Santa Barbara) Phys.Rev.Lett.57:2244-2247. This paper maks the start of a new orientation in Quantum Gravity, so perhaps you could want to set the milestone here.

Anyway, FIND DK QUANTUM GRAVITY AND TOPCITE 500+ AND DATE BEFORE 1985 gives only ten papers. And three of them are actually "Quantum Theory of Gravity", by Bryce S. DeWitt, in 1967.

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answered Oct 26, 2011 by anonymous [ no revision ]
Upvoted for the Spires search. Those papers were exactly the sort of thing I was looking for. The Ashtekar paper is a 4 page PRL, and consequently says next to nothing about the history.

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@user388027, the prejudices you ask about are an outcome of early attempts to quantize gravity, they are unlikely to be discussed as part of these early attempts. I think one of my problems of figuring out what you are asking for precisely is that your point 1+2 are not the same, and in fact contradict point 3. Are you asking about early attempts to quantize gravity, or are you asking which expected features of quantum gravity resonate best with string theory? those are two separate questions.

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BTW, thanks to the anon user who edited the spires link to do it clickable :-D

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@Moshe: Yes, I didn't express myself well. What I want to do is read through early attempts to grapple with quantum gravity in order to see how the 'prejudices' which string theory satisfies emerged.

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Ok, but common lore like the one I tried to specify in my answer, will not have been explicitly written anywhere at that time. Anyhow, in my mind, the Dewitt papers were the most influential ones, not a bad place to start.

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Upvoted because arivero's answer supplies concrete citations. I'd like to commend also Ashtekar's work with Troy Schilling on non-relativistic non-Hilbert quantum dynamical state-spaces (arXiv:gr-qc/9706069v1).

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Accepted answer for the SPIRES search.

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In 1983 a "generic high energy theorist" would have known that superstring theory could describe quantum gravity. However, they could have thought superstring theory was anomalous or they could have thought it was not anomalous. The Green–Schwarz mechanism, the anomaly cancellation mechanism in type I superstring theory with the gauge group SO(32), was discovered in 1984.

In 1983 a "generic high energy theorist" could have thought quantum gravity based on general relativity was perturbatively renormalizable or they could have thought is was not perturbatively renormalizable. Quantum gravity based on general relativity was proven to be perturbatively non-renormalizable by Goroff and Sagnotti in 1985.

In 1983 a "generic high energy theorist" could have thought supergravity with N supersymmetries in D dimensions was perturbatively renormalizable or they could have thought is was not perturbatively renormalizable. As far as I know, this is still not settled for some N and some D. See for example Green.

In 1983 a "generic high energy theorist" would have known nothing about Ashtekar variables and thus Loop quantum gravity, and all related formalisms, as Ashtekar variables were discovered by Ashtekar in 1986.

As you can see, the "modern" picture of quantum gravity only started to emerge around 1986. In 1983 a "generic high energy theorist" could have believed almost anything about quantum gravity.

Oh, a good, but old, review of pre 1983 views of quantum gravity is Ashtekar and Geroch written way back in 1974!

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answered Oct 27, 2011 by Kelly Davis (220 points) [ no revision ]
Also, a GHET in 1983 could be interested on supergravity only because of the turmoil caused by Witten 1981 "Search for a realistic Kaluza-Klein theory". For instance A. Salam got very interested and a good bunch of his team was mobilized to study this particular subtopic.

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And a personal thinking: a hep-th theorist could be more inclined towards strings for gravity that a gr-qc one, because the later are used to think of Riemann tensor as a [set of] bidimensional object[s], so to them it is not so surprising that a 1+1 worldsheet can feel gravity. My guess is that Gr-Qc practicioners probably felt initially that strings were just a very convolved way to measure curvature.

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