An Exceptionally Simple Theory of Everything

[Jim Kata]

Thankfully, I'm not afraid of looking ignorant

My knowledge of representation theory and octonions is very limited and definitely not up to snuff to understand all of this paper like taking a real non compact representation of e8 but the thing I find the most interesting is triality.

Another thing is like, Hans and Carl pointed out, the possible connection between tribimaximal matrix and the matrix Garrett uses to embed the su(3) root system into so(6).

I have two questions one is off the wall and one is??

1.) The matrix in Garrett's paper, as he says, can be viewed as the twelve midpoints of the edges of a cube. Now I was not really thinking, but there are 12 leptons, and flavours of quarks, four for each generation. Do these midpoints on the edges of this cube represent each of the generations of quarks and leptons? I wish I could draw what I mean.

2.) Looking at figure 5 this theory seems to predict right handed leptons. Is this true? If so, is there a mechanism to explain why these are not observed?

 

[marcus]

Peter Woit blogged Garrett's paper
http://www.math.columbia.edu/~woit/wordpress/?p=617
as well he might
as for the arxiv gnomes reclassifying the paper from hep-th to gen, fill in the consonants
_acques _ucques.
It's infuriating and depressing that someone at arxiv would stoop to something that dishonorable.

For this reason, and for its merits, I hope we choose this paper as our PF "Beyond" forum Paper of the Year.
It is a small thing but we should have some way, even a small symbolic one, of fighting back.

 

[jal]

I see that garrett is carrying on simultaneous conversations in at least 3 places.
I have an observation that might help the beginners.
----------
Is there anyone out there capable of reading a knitting pattern?
You need to know the symbols for each action of the needles and when you apply that action a pattern will emerge.
The needles are flying off into the 3rd dimension and picking up the threads and leaving the threads in a 2d pattern.
There are moves that cannot be done.
Talk to a grandma.
E8 is a template for a knitting pattern. The pattern exists in our perceived 3d.
CERN will be able to look for the patterns that exist from 10^-15 to 10^-18. It will not be able to see the movement of the “needle” doing its dance that created the pattern. LQG will be needed to find out what the “needles” are doing.
I cannot knit, I cannot do LQG and much less E8.
However, if you succeed in writing the knitting pattern, grandma will be able to knit it.
----------
Ref.:
Proton
Mass m = 1.00727646688 ± 0.00000000013 u
Mass m = 938.27203 ± 0.00008 MeV [
Charge radius = 0.875 ± 0.007 fm
(diameter of about 1.6 to 1.7×10−15 m [1], and a mass of 938.27231(28) MeV/c2 (1.6726 × 10−27 kg), 1.007 276 466 88(13) u)
Mean life τ >10^31 to 10^33 years

 

[marcus]

Garrett, want to clarify about the dimension? (for the not too smart spectator)
Baez when he talks about E8 says dimension 248
but I add 222 and 18 and get 240. So I am off by eight.

Just on a general level here is a paragraph on page 27 that I like a whole lot, and any comment or amplification from you would be welcome:

It should be emphasized that the connection (3.1) comprises all fields over the four dimensional base manifold. There are no other fields required to match the fieelds of the standard model and gravity. The gravitational metric and connection have been supplanted by the frame and spin connection parts of A.

The Riemannian geometry of general relativity has been subsumed by principal bundle geometry---a significant mathematical unification.

Devotees of geometry should not despair at this development, as principal bundle geometry is even more natural than Riemannian geometry. A principal bundle with connection can be described purely in terms of a mapping between tangent vector fields (diffeomorphisms) on a manifold, without the ab initio introduction of a metric.

these 8 missing dimensions, in my bad arithmetic, are they the "frame and spin connection parts of A" referred to above---or what, in simple terms, happened to them?

Hey people! Just by the way without the ab initio introduction of a metric means background independent. We are talking about background independent QFT which was, I guess, the whole idea in the first place. It's not surprising if some people are looking pretty happy at this point.

 

[garrett]

Hi marcus,

The other eight Lie algebra elements are the basis elements of the Cartan subalgebra, so they're technically not included with the other roots. They are physical fields though -- six of them are standard and two are new.

With that paragraph you quote, I was saying something I think is important, but might not be widely known by physicists. Conventional GR requires a metric to exist over the manifold -- this is kind of a strange object from the point of view of differential geometry. Nevertheless, physicists are used to thinking of GR as geometric and Yang-Mills as involving algebra. However, Lie algebra elements correspond to vector fields over the Lie group manifold. And a principal bundle can be described purely in terms of maps between vector fields, without a metric, using a tangent vector valued 1-form field over the entire space. In this way, the geometry of principal bundles is more natural than Riemmannian geometry. But this is a very subtle point, and I don't expect it to mean much to most readers.

 

[strangerep]

[Lubos's] only rational attack is based on the Coleman-Mandula theorem, the abstract of which he kindly provides a link to, but evidently didn't read, since the first assumption of the C-M theorem is stated there in the abstract, and doesn't apply in the case at hand, as stated in the paper.

Hi Garrett,

I don't understand the details of your dismissal of the C-M theorem. IIUC, you're basically
saying that it doesn't apply because in your setup we have deSitter instead of Poincare
(right?).

If so, then here's the thing that seems strange to me: deSitter contracts to Poincare
(for $\lambda\to 0$). Contraction is process of continuously changing the
structure constants. Pretty much everything else about the Coleman-Mandula theorem
seems to respect some form of continuity (analytic S-matrix, use of infinitesimal generators, etc).
So if you're relying on deSitter, then shouldn't we get negligible scattering unless
$\lambda$ is significant?

Or am I naively expecting too much from continuity?

 

[garrett]

Strangerep, you have hit the nail on the head. This E8 Theory, which includes MacDowell-Mansouri gravity as an integral part, is not defined for $$\Lambda=0$$.

 

[Haelfix]

I was the anonymous person who brought up CM in Bee's thread.

And I am still a little disturbed by it. Desitter space has no Smatrix, and if the action perse (MM) explicitly forbids contraction to regimes where CM applies, I can't see how you will recover the effective standard model field theory.

Read there is no apparent Smatrix in the theory!

Moreover even if there exists such a thing in the theory, I don't see how you will suppress unitarity violating interactions absent imposing a hard cutoff that generates gauge anomalies b/c it breaks the Desitter group. You need to run a general operator analysis to sort the mess out.

The topological sector of your theory is highly nontrivial as well, and I can't see how you will suppress all sorts of very bad instanton processes.

 

[garrett]

I was the anonymous person who brought up CM in Bee's thread.

That's fine, it's certainly not a stupid question.

And I am still a little disturbed by it. Desitter space has no Smatrix, and if the action perse (MM) explicitly forbids contraction to regimes where CM applies, I can't see how you will recover the effective standard model field theory.

It's going to have to be an approximation.

Moreover even if there exists such a thing in the theory, I don't see how you will suppress unitarity violating interactions absent imposing a hard cutoff that generates gauge anomalies b/c it breaks the Desitter group. You need to run a general operator analysis to sort the mess out.

The topological sector of your theory is highly nontrivial as well, and I can't see how you will suppress all sorts of very bad instanton processes.

Why do you think I published the paper? I can't do everything myself.

And I'm first to admit this is just the beginning of a theory that might be wrong.

 

[Haelfix]

Don't get me wrong, that's fine. I happen to love E8 anyway, its a beautiful group

 

[marcus]

I was the anonymous person who brought up CM in Bee's thread. .

It would be great to have more discussion about Coleman-Mandula. On Bee's thread the first mention I could find was Moshe around noon pacific on the 7th
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html#c978188498139402984

At 12:38 PM, November 07, 2007, Moshe said...

Two quick questions:

1. What is the loophole in the Coleman-Mandula theorem used in this construction? note that the theorem allows constructing theories where internal and spacetime symmetries are unified, as long as those theories are free.

2. When packaging bosons and fermions together, at least one set of fields will have the wrong spin statistics relation. In addition to violating unitarity etc., this definitely is not what is going on in the standard model.

It led to quite a bit of discussion, some of which was echoed a couple of days later over at Peter's
==quote Woit's blog==
# more questions Says:
November 9th, 2007 at 6:57 pm

As long as Coin is asking questions, I didn’t understand (1) why this doesn’t violate the Coleman-Mandula theorem, and, (2) what about the nonrenormalizability of GR?

----

# Coin Says:
November 9th, 2007 at 7:24 pm

MQ, Garrett does seem to offer an argument concerning your (1) in a reply to Moshe in the comments section of the Backreaction post:

1. Yes, the Coleman-Mandula theorem assumes a background spacetime with Poincare symmetry, but this theory doesn’t have this background spacetime — with a cosmological constant, the vacuum spacetime is deSitter. So this theory avoids one of the necessary assumptions of the theorem, and is able to unify gravity with the other gauge fields. On small scales though, Poincare symmetry is a good approximation, and on those scales gravity and the other gauge feels are separate, in accordance with the theorem. (I’m not the first person to dodge C-M this way.)

Several more posts over the course of that thread drill down on this point further…

---

# Garrett Says:
November 9th, 2007 at 7:26 pm

more questions:

(1) The first person I know of to point out this loophole in Coleman-Mandula was Thomas Love (a visitor here) in his 1987 dissertation. There is also a discussion of this loophole in this recent paper by F. Nesti and R. Percacci: Graviweak Unification. Or you can go to the source and look at Coleman and Mandula’s paper, in which their first condition for the theorem is “G contains a subgroup locally isomorphic to the Poincare group.” The G = E8 I am using does not contain a subgroup locally isomorphic to the Poincare group, it contains the subgroup SO(4,1) — the symmetry group of de Sitter spacetime.

(2) I’m banking on the LQG community to crack this one. So multiply the odds of this E8 Theory being right times the odds of LQG finding the right answers for quantizing the theory… and I’m first to admit it’s a long shot. But I think it’s got a chance, which is why I work on it.
==endquote==

In his reply Garrett gives links for the Percacci-Nesti paper and for the Coleman-Mandula one.
I for one could use any further discussion of Coleman-Mandula that comes along and what especially interests me is that John Baez spent several weeks here at Beyond forum convincing us that the right local symmetry group for quantum field theory was SO(4,1) and not the Poincaré.
And I was convinced. So when people sound as if they think Garrett is fudging by using the deSitter group as an inferior substitute---to dodge the C-M no-go obstacle---then I wonder because it seems to me the reverse. It is the older work which uses the inferior substitute and this new work uses the RIGHT local symmetry.
And Colemandula be damned. If this is dumb, please help me see why.

 

[jal]

I want to bring your attention to a drawing.
https://www.physicsforums.com/attachment.php?attachmentid=11509&d=1194846037
posted by Hans de Vries at

https://www.physicsforums.com/showthread.php?p=1501369#post1501369

If you do the same thing for E8, the shadow of the 3d construction produces the familiar E8 pictures.
A search, using “image”, will find it.
-------------
The 3d construction, if orientated properly, produces the tetras.
The hard question ….
Since a 3D construction of E8 can produce the 2D construction, What is the obstacle to assuming that the E8 is a construction existing in 3D?

 

[garrett]

E8 lives in 8D. Sure, it can be projected down to 3D. It then needs to be projected to 2D to be shown on a screen or paper. If we used holograms instead of screens, I'd be making tons of 3D plots. But, as it is, I just project from 8D to 2D, because if I go from 8D to 3D to 2D, the perspective would make a mess of things.

 

[Hans de Vries]

I want to bring your attention to a drawing.
https://www.physicsforums.com/attachment.php?attachmentid=11509&d=1194846037
posted by Hans de Vries at

https://www.physicsforums.com/showthread.php?p=1501369#post1501369

That image was generated with the (freeware) ray-tracer Povray.
All the projections come for free It's just setting up three light
sources on the principle orthogonal axis.

So the projections are actually shadows. You can give them colors as
I did by using transparent colored objects and/or colored light sources.Regards, Hans

 

[Hans de Vries]

It would be great to have more discussion about Coleman-Mandula.

Indeed, Theorems like that of Coleman and Mandula could be in
the same league as Lorentz invariance and Gauge invariance, with
respect to the guidance they can bring.

Weinberg handles the proof in appendix B of the first chapter (ch:24)
in Volume III handling the possible internal symmetries in combination
with the Poincaré group. Haven't studied the proof though ...

I don't think you can really "circumvent" Coleman Mandela by going
to another space-time group. You'll have to deal with the appropiate
version of the theorem for that specific group instead. I don't know
if there exist something along that line for SO(4,1). Weinberg refers
to chapter 32, the last chapter in Vol.III, for the application of
Coleman Mandela to higher dimensional spaces and he mentions
p-brane theories where the Theorem "does not apply"


Regards, Hans

 

[CarlB]

With that paragraph you quote, I was saying something I think is important, but might not be widely known by physicists. Conventional GR requires a metric to exist over the manifold -- this is kind of a strange object from the point of view of differential geometry. Nevertheless, physicists are used to thinking of GR as geometric and Yang-Mills as involving algebra. However, Lie algebra elements correspond to vector fields over the Lie group manifold. And a principal bundle can be described purely in terms of maps between vector fields, without a metric, using a tangent vector valued 1-form field over the entire space. In this way, the geometry of principal bundles is more natural than Riemmannian geometry. But this is a very subtle point, and I don't expect it to mean much to most readers.

Is this referring to the work by the Cambridge geometry group?

http://www.mrao.cam.ac.uk/~clifford/publications/abstracts/gravity.html

 

[garrett]

No Carl, you're not that lucky. I was referencing this:

http://deferentialgeometry.org/#[[Ehresmann principal bundle connection]]
http://en.wikipedia.org/wiki/Ehresmann_connection

 

[garrett]

Also, I'll be presenting a talk tomorrow, bright and early:

http://relativity.phys.lsu.edu/ilqgs/

The pdf for the talk just went up five minutes ago, but there seems to be some problem displaying them on windows machines. If anyone has any suggestions on how to fix that, it would be appreciated. (I have a mac)

 

[CarlB]

This windows machine displays the Acrobat file beautifully. It makes a good addition to the arXiv article. It used to be my experience that very large Acrobat files (the above is 1.8MB) should be downloaded rather than opened directly.

 

[Hans de Vries]

Also, I'll be presenting a talk tomorrow, bright and early:

http://relativity.phys.lsu.edu/ilqgs/

The pdf for the talk just went up five minutes ago, but there seems to be some problem displaying them on windows machines. If anyone has any suggestions on how to fix that, it would be appreciated. (I have a mac)

Success with your talk Garrett. You might say that you "have set the stage" now,
more then you probably would have imagined.


Regards, Hans

 

[garrett]

Thanks Hans, you're not kidding. I'm looking forward to going back to being a hermit again after tomorrow, playing with equations instead of with people.

I think we worked out the pdf problem. Thanks for the tip though Carl.

 

[jal]

E8 lives in 8D. Sure, it can be projected down to 3D.

Well ... it's better than dealing with 11D.
Believe me ... I'm trying with what I got ...?
From your statement I get a visual of a proton iceberg.
I looked at your slides ... it should give an interesting presentation.

 

[marcus]

...I'm looking forward to going back to being a hermit again after tomorrow, ...

It's been wonderful being able to watch the baby debut. thanks for being here at PF during.
Really smart of Jorge Pullin to invite you immediately to do ILQGS. It is already starting to be runup to next July QG².

On your sllde #45 in the concluding "discussion of E8 theory" section you say

Quantization:
* Coupling constants run.
* Large Lambda compatible with UV fixed point.
* Just a connection — amenable to LQG, spin foams, etc.

In Reuter's papers Lambda indeed gets large as k -> infty, so he has Lambda run in the right direction for E8 theory's needs.

But the other constant he has running is G_Newton which he has go to zero (!) as k -> infty. It seems like an unexpected thing that might cause a stumble, so I mention in case you get into discussing that bullet of slide 45.

Have fun with the ILQGS talk! it will be good for both theories and I hope they can converge some.

 

[strangerep]

Desitter space has no Smatrix, [...]
Read there is no apparent Smatrix in the theory!

Hi Haelfix,

I have some followup questions (for yourself, or anyone else who
knows the answers)...

Where can I read more about how DeSitter space has no S-Matrix?
I'm interested in the precise assumptions that lead to that conclusion.
Is the answer trivial in that, if one looks backwards in an expanding space,
there's no such thing as infinitely-separated effectively-free particles
for $t \to -\infty$? Or is there more to it than that?

If the former, I'm wondering how Garrett could get any cross-sections
out of such a theory which could be meaningfully compared with particle
physics experiments.

For that matter, what are the Casimirs and unitary irreps for the DeSitter
group? I tried some googling, but couldn't find a good exposition of this.

 

[marcus]

...Where can I read more about how DeSitter space has no S-Matrix?
...
Is the answer trivial in that, if one looks backwards in an expanding space,
there's no such thing as infinitely-separated ...

It'll be interesting to see what Haelfix says. Thanks for asking. About your guess of a trivial explanation, note that deSitter space contracts and then expands, so if you look back in time you can have infinitely separated paths.

but even without that, after two particles are a lightyear apart who cares? S-matrix could still be a good effective approximation, even if local reality is deSitter shaped. Just my two cents. We'll see what Haelfix says.

 

[Haelfix]

Bryce De Witt afaik did a lot of early work on DeSitter space, but I don't really feel like tracking down the references.

Instead there's a readable bit by Witten on it
http://arxiv.org/PS_cache/hep-th/pdf/0106/0106109v1.pdf

Its a little short on details, but he's at least attempting to recover some notion of observables. Yes the main problem is there is there is no good notion of spatial asymptotia nor is their a conformal null boundary. The former could give you correlation functions on the boundary (alla AdS), the latter an SMatrix (Minkowski)

To quote

"The problem with de Sitter space can actually be divided into two parts. One aspect
is that because of the horizon experienced by an observer, one cannot hope to witness
the final state of the whole universe. The other side of the problem, which seems more
acute to me, is that, as indicated above, one also cannot in de Sitter space make sense
in a precise way of what we usually regard as local particle physics quantities. (...) However, an observer in such a universe would have to perform all
experiments with a finite supply of elementary particles and free energy stored up before
the acceleration progresses too far. Under these conditions, it seems doubtful that one
could perform asymptotically precise measurements."

DeSitter space is nasty indeed... Its the biggest theoretical problem imo of this century.

 

[marcus]

Hi Haelfix, I was wondering if you would quote that 2001 paper of Witten. Here is a long quote from the page before where you quoted, which explains WHY he is worried about civilization in the future being able to measure stuff with very high precision in an expanding universe, particularly one with positive cosmological constant.

==quote Witten==
In an eternal universe, in the absence of gravity, with a constant free energy supply generated by stars, this makes perfect sense. In a more realistic description of nature, taking the expansion of the universe into account, there are many pitfalls.

De Sitter space (or a cosmology asymptotic to it in the far future) is a particularly unfavorable case for achieving the usually assumed degree of precision. For example, if it is true that the dimension of the quantum Hilbert space is finite, this puts a limit on the conceivable complexity of any experimental apparatus or computational machinery. The
inflation that will occur in the future in de Sitter space puts a limit on the time in which the experiment must be conducted (or the computation performed) before the free energy supply runs down.

Even the concept of an observer in de Sitter space as a living creature making an observation has only limited validity. For life itself is only an approximation, valid in the limit of a complex organism or civilization. There might be a cosmology in which the approximation we call life is better and better in the future, but this requires a process of
adaptation to longer and longer time scales and lower and lower temperatures [15], neither of which is possible in de Sitter space (where inflation sets a maximum time scale, and the de Sitter temperature is a minimum temperature). The approximation we know as life thus breaks down in the far future in an asymptotically de Sitter world, and this will put an end to any measurement (or computation) performed by an observer or civilization in such a spacetime, and hence an upper bound to its precision.

==endquote==

As one can see, his argument is somewhat speculative. It does not present, as far as I can see, any problem with deSitter space or a universe with positive Lambda. Rather it points out problems inherent in human theories which depend on giving meaning to precise asymptotic measurement----measurement at infinity. They don't apply to the world we live in.

The sensible response would seem to be NOT to avoid a particular shape, if it fits our universe, but to go with the observed shape and FIX THE THEORY. I see that as the lesson to be drawn from Witten's paper. So I don't see Witten's paper as particularly relevant to present discussion of E8 theory. Do you agree?

the paper is http://arxiv.org/hep-th/0106109
an expanded version of the talk Witten gave to Strings 2001 at Mumbai, India.

for an updated view of what the future of scientific measurement looks like in the universe we got, see
http://arxiv.org/abs/0704.0221
The Return of a Static Universe and the End of Cosmology
Lawrence M. Krauss, Robert J. Scherrer
Gen. Rel. Grav. 39 (2007) 1545-1550

it seems considerably more dismal than the view Witten evokes

We demonstrate that as we extrapolate the current LambdaCDM universe forward in time, all evidence of the Hubble expansion will disappear, so that observers in our "island universe" will be fundamentally incapable of determining the true nature of the universe, including the existence of the highly dominant vacuum energy, the existence of the CMB, and the primordial origin of light elements. With these pillars of the modern Big Bang gone, this epoch will mark the end of cosmology and the return of a static universe. In this sense, the coordinate system appropriate for future observers will perhaps fittingly resemble the static coordinate system in which the de Sitter universe was first presented.

 

[marcus]

DeSitter space is nasty indeed... Its the biggest theoretical problem imo of this century.

I don't understand what you are saying. Witten's vision of scientific measurement in distant future applies to the standard LambdaCDM cosmology which describes the world we live in, in the same way it applies to the simplified deSitter model of it.

How can you call the real world nasty (as it must be by the same reasoning)? Maybe you are joking.

 

[Haelfix]

Strangerep asked me about the Smatrix in DeSitter space, so I gave him a paper that tries to explore that.

The relevance is there are no quantum observables (neither local, asymptotic or global) in quantum gravity in DeSitter space. People, like Witten (and others) look for some, but they are hard to construct. Some people use relational variables instead and so forth. Even the nature of the Hilbert space is under dispute (eg is it finite dimensional or infinite), nor do we know what the unitary reps are.

There is nothing speculative about this, that's the state of the art, and hasn't progressed that much for over 30 years b/c of the technical problems with dealing with the space.

The relevance to the E8 paper (which is essentially a classical paper) is in the quantum regime you want to seemlessly connect local DS to local Poincare for lambda --> 0 in the standard model limit. Which is hard to do! Not only b/c of the absence of an SMatrix in the gravity regime, but b/c it already seems like there is a discontinuity in the very action.

 

[marcus]

Also, I'll be presenting a talk tomorrow, bright and early:

http://relativity.phys.lsu.edu/ilqgs/

The pdf for the talk just went up five minutes ago, but there seems to be some problem displaying them on windows machines. If anyone has any suggestions on how to fix that, it would be appreciated. (I have a mac)

This new PDF is a big help. CarlB's comment was that "It makes a good addition to the arXiv article."

Here is the direct link to the PDF.
http://relativity.phys.lsu.edu/ilqgs/lisi111307_2.pdf
Here is the direct link to the audio.
http://relativity.phys.lsu.edu/ilqgs/lisi111307.wav

======EDIT TO REPLY TO NEXT=====
Thanks Carl, interested by the possible preon angle. I wrote you a PM in reply.

 

[CarlB]

Marcus, I'm beginning to suspect that there is a fairly simple preon model hiding behind the E8 here. The paper on octonions by Baez:
http://math.ucr.edu/home/baez/octonions/oct.pdf

shows that E8 is related to the isometries of OxO where O is the octonions. The octonions are not associative, but they are close. If you could adjust the signs in the multiplication table, they would be associative. They are called "alternative" instead of the more general non associative.

When you translate spinors into density operators, you take two of them at a time. This gets rid of arbitrary signs in the spinors, they cancel. This means that when you translate octonionic symmetry operations on spinors into octonionic symmetry operations on density matrices, you end up with a density operator theory that IS associative.

Associativity is important in density matrix theory because it translates into the fact that when you compute a path integral, it doesn't matter whether you start your analysis at the initial and final end.

Another way of saying the same thing is that when you compute the probabilities associated with a system that transitions through the sequence of states A, B, and C, it doesn't matter if you do the computation as (AB)C or A(BC), you should get the same result. And the octonions are compatible with this, when you apply them to density operators (as are required for virtual particles anyway).

So the OxO translates into E8 being a model of composite particles made from two quantum objects with |O| symmetry, where "|O|" symmetry is a density matrix type symmetry you get from (more or less) ignoring signs in the octonions.

 

[Thomas Larsson]

The relevance is there are no quantum observables (neither local, asymptotic or global) in quantum gravity in DeSitter space.

Unless, of course, we are missing something essential.

It should be an uncontroversial fact that diffeomorphism symmetry on the circle *is* compatible with locality, in the sense of correlators depending on separation, but only in the presence of an anomaly; unitary Virasoro reps with h > 0 exist, but only if c > 0. This observation was the main reason why I generalized the Virasoro algebra to higher dimensions.

With local observables, it does not really matter if de Sitter admits global observables or not.

 

[Hans de Vries]

Where can I read more about how DeSitter space has no S-Matrix?

Is the answer trivial in that, if one looks backwards in an expanding space,
there's no such thing as infinitely-separated effectively-free particles
for $t \to -\infty$? Or is there more to it than that?

It seems to be just that...

http://online.kitp.ucsb.edu/online/strings98/witten/

The thing what really does seem to hurt is this:

http://online.kitp.ucsb.edu/online/strings98/witten/oh/12.html

$$\Lambda = 0\ \Rightarrow\ \mbox{S-matrix}$$

$$\Lambda < 0\ \Rightarrow\ \mbox{AdS/CFT}$$

$$(\Lambda > 0\ \Rightarrow\ \mbox{no AdS/CFT...})$$

He's getting more cautious now here:
http://online.kitp.ucsb.edu/online/strings98/witten/oh/25.html


Regards, Hans

 

[ccdantas]

Audio for today's talk by Garrett Lisi is posted at
http://relativity.phys.lsu.edu/ilqgs

 

[marcus]

Audio for today's talk by Garrett Lisi is posted at
http://relativity.phys.lsu.edu/ilqgs

I've been listening! It's impressive and nicely done. I hear Jorge Pullin but not much interruption by questions so far.

the phrase "suggestively colored dark" commenting on slide #38 is suggestive

this was in reference to the "xPhi" and the "w" symbols at the bottom of the E8 Periodic Table on slide #38.

we have company coming and my wife insisted that I stop listening and help her bake an almond cake
so I only got to hear the first 38 of the 48 slides discussed.