# Alejandro and the graviton

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Alejandro recently submitted a post at SPS which engaged the active attention of Lubos Motl. So much so that unless one has sharp eyes one cannot see Alejandro's original post-----there are so many "moderator notes" inserted by Lubos.

this means Alejandro's original post probably has some interesting points, so let us reconstruct it here (without the L.M. comment) so we can see the overall tenor of it----after that we can consider what L.M. interjected, and how Alejandro replied and so forth. Here is the reconstructed original:

----quote from arivero---
Some days ago, in another forum, Urs wondered why some of us are very
positive about the relationship between strings and gauge theory but
we are not excited about the point of strings "knowing gravity".
[1]
Yep, if one thinks about it, it is surprising that I am not surprised.
Perhaps it is because string lessons do not derive, as far as I have
read, Einstein-Hilbert action in some limit.
[2]
Most teachers just show a sort of consistent spin two particle and they
say "see, the graviton here". Some others note that string is about
word-sheet actions, thus it contains a constant having the dimensions
appropiate to measure curvature. But neither spin two nor curvature or
area are definitive signatures of our gravity. It is possible to formulate
a curvature theory for other approximations to Einstein gravity, for
instance for Newtonian gravity.
[3]
Perhaps related to this doubt, note that also Electroweak Theory has a
non-renormalisable, area-like, constant: fermi constant. But it does
not have spin two particles by itself.
[4]
And one could devise some ways
to formulate EW theory, or even electromagnetism, as a worldsheet
action theory, thus sort of strings.
[5]
But I do not see how a elementary spin two field would be forced by using
these formulations.
[6]
Alejandro

--------------end quote--------
I have put numbers as pointers to the "moderator notes", which I will fetch so we can see the general tenor of them as well.

## Answers and Replies

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----quote from SPS moderator notes---
[1]
[Moderator's note: I thought that Edward Witten experienced the strongest
intellectual thrill in his life when he learned how string theory
predicts gravity, and Witten is not the only one. ;-) LM]

[2]
[Moderator's note: Good textbooks and lectures of string theory - e.g.
chapters 3 of Green+Schwarz+Witten and of Polchinski - derive that
the background metric must satisfy the correct Einstein equations if
the worldsheet theory is conformal i.e. consistent. They also explain
that the same effective action is seen by the scattering of the
perturbations - namely by the gravitons. This is such a basic feature
of string theory - and a key motivation to study that I would say
that someone who has not this calculation does not really know
what string theory is at the technical level. LM]

[3]
[Moderator's note: One can show the correct mass (zero), correct spin
(two) and correct interactions of the graviton in string theory.
Moreover, the correct interactions at low energies are guaranteed by
the consistency of the theory - general relativity is the only way how
to define consistent nonzero couplings of massless spin two particles
in a (special) relativistic theory. Because string theory defined as
a worldsheet theory can be shown to give a consistent spacetime theory,
the spacetime theory must automatically contain the right interactions
at long distances, and explicit calculations show that this is indeed the
case. LM]

[4]
[Moderator's note: Why should the electroweak theory have spin two
particles? LM]

[5]
[Moderator's note: Certainly not as anything analogous to string theory as
we know it. String theory, in the conventional meaning of the word,
always automatically includes gravity, and it is unique - once the five
different perturbative versions are unified. The idea that one can make
a consistent string theory that gives "electroweak theory only" is
a misunderstanding of basics of string theory. What sort of "new" string
theory do you have in mind? I think that this is a very popular laymen's
misunderstanding - they often think that it is possible to modify string
theory in hundreds of ways and define hundreds of different sibblings of
string theory. No, string theory - or a theory of quantum gravity -
is unique. LM]

[6]
[Moderator's note: An elementary spin two field is described by a tensor
with at least two indices, say . Some of the components of this
tensor would lead to negative-norm states - namely the mixed time-space
components. There must be a gauge symmetry that removes these unphysical polarizations and (linearized or nonlinear) general covariance is the only possible gauge symmetry that can remove these states, and still lead to nonzero interactions. Just try to find a different solution, and you
will see that you fail. LM]

-----end quote----

I suppose the first interesting thing one notices is that the moderator notes are somewhat longer than the original post from Alejandro.

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But Marcus how would we understand the continuing evolution of theoretical positions for laymen like me, if we did not have Lubos respond to what Arivero writes? Your having a hard time with me as it is, and my thick head sometimes

If you noticed, Lubos also took parts of his responses from other posts and repasted them in arivero's post. A sure sign to me, he is drivng the point home

I had a addition link by arivero that I showed today as well that might be of interest to you, in terms of parameters, of natural numbers.

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the exchange has now continued several more posts and Alejandro says he is convinced by LM and will read Chapter 3 of Green,Schwarz,Witten textbook and also Chapter 3 of Polchinski textbook. thanks to Lubos for the kind and lengthy exposition.

anyone interested in the whole exchange of posts [and moderator notes]
can read the full thread in SPS

the thread is called "not surprised about the graviton?"

this thread focuses the spotlight on the issue of to what extent and how
is string theory supposed to "know" about gravity.

For me, although not party to the discussion at SPS, the abiding question continues to be: if gravity is an effect of the (highly variable) geometry of spacetime----in other words if it is NOT the effect of forces mediated by particles-----then in what sense can a theory with a rigid background geometry model gravity?

What has repeatedly impressed me, as I listen to discussions like this, is the extent to which the evidence offered for stringy knowledge of gravity resemble Omens or signs of Good Things to Come.

A graviton, I take it, is not something that a string theorist would impute to nature as something that actually exists----rather it is something that appears in the analysis when a flat approximation is made using Minkowski space or some other artifical convenience.

It was at one time customary for a Roman official called the Haruspex to consult the entrails of a rabbit and if he found favorable omens then you would go ahead with whatever it was.

In the String theory case, the Haruspex examines the entrails of Minkowski space and discovers a graviton----this then is a favorable omen.

-------quote from LM note [2]----------

...the background metric must satisfy the correct Einstein equations if
the worldsheet theory is conformal i.e. consistent. They also explain
that the same effective action is seen by the scattering of the
perturbations - namely by the gravitons....

-----end quote----

the gravitons, one sees here, are equated with the "perturbations" which are something that occurs in the analysis using a rigid (usually flat) background. One sets up an artificial rigid spacetime framework chosen from a menu, and then one twangs it. The twangs or ripples are the perturbations superimposed on the background. these are the "gravitons".

If the background were fully dynamic one imagines one would not want or need gravitons.

At another point the moderator note [2] says "the background metric must satisfy the correct Einstein equations". This prompts me to reflect that
if the background is flat spacetime---Minkowski space---that is a particular solution of the Einstein equations for the special case when there is no matter or energy in the universe!

This is certainly a good approximation to Nature wherever there is not much matter or energy around, although I doubt anyone would call it a realistic solution.

Haelfix had a good post about these quandaries in another thread. i will try to locate a link for it.
[edit: yes here is the Haelfix post]

Meanwhile, many thanks to Lubos Motl for such careful and enlightening comments, and cordial thanks as well to Alejandro for giving Lubos the occasion to hold forth!

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Marcus I think the snarky haruspex references are unfair to string physics. Historically they pursued quantized strings for other reasons and did it in the standard way, in terms of flat Minkowski relativity. And lo and behold the graviton, all unlooked for, fell out of their theory, a great new thing. And AFAIK graviton physics cannot be distinguished from GR physics with present day experiments.

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Marcus I think the snarky haruspex references are unfair to string physics. Historically they pursued quantized strings for other reasons and did it in the standard way, in terms of flat Minkowski relativity. And lo and behold the graviton, all unlooked for, fell out of their theory, a great new thing. And AFAIK graviton physics cannot be distinguished from GR physics with present day experiments.
It was kind of snarky to mention haruspices wasnt it? Yes not really fair. And I would guess that you are right. Present-day experiments would not be able to tell real GR physics from graviton physics.

Perhaps it would only be distinguishable if you actually had a black hole or a big bang in your living room. I suppose it is primarily in those rare cases when you have a highlycurved space that graviton physics doesnt do a good imitation of the real thing, or when geometries change as stars collapse.

Historically too you I suspect you are right---indeed I suppose that the original string people were brilliant and courageous. The Haruspex image was not historical in nature but came to mind when I imagined a latterday light taking one of us aside in 2004 to interpret the omens for him. "We have examined the graviton and behold it is a Sign we are on the Right Path."

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marcus said:
I imagined a latterday light taking one of us aside in 2004 to interpret the omens for him. "We have examined the graviton and behold it is a Sign we are on the Right Path."
And when it fell out for them, they did take it as such a sign. It had a tremendous effect, converting physicists who were working on other things to stringiness. Likewise the discovery of the superstrings was a blast (Feynmann danced when he heard there was only one superstring theory, but then they discovered the others). And the discovery of the dualities and the glimpses of non-pertubative M-theory have been a sign unto them too, as is Maldacena's discovery of the holographic principle.

It might be a hit on string physicists that they live from wonder to wonder and become defensive when there hasn't been one for a while. But the critics are always there, and they are only silenced by a new miracle. Nobody hurts more than the string crowd because their string physics is too energetic for today's experiments to test it.

arivero
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sol2 said:
But Marcus how would we understand the continuing evolution of theoretical positions for laymen like me, if we did not have Lubos respond to what Arivero writes? Your having a hard time with me as it is, and my thick head sometimes
Well, IMHO it should be more readable if s.p.s used the conventional > quotation sign instead of bracketing everything, that is true.

And yes, I went this morning to the library to get the books, I borrowed the old GSW and glanced Polchiski. I'd say that the real claim is that strings are able to quantise a 26 dim Kaluza-Klein theories or 10 dim supersym ones with very specific matter sources. This is not exactly as to quantise 4dim gravity, but well I think that 26 dim gravity is also non renormalisable, is it?

I had a addition link by arivero that I showed today as well that might be of interest to you, in terms of parameters, of natural numbers.
Not my theory, but De Vries' one. Interesting anyway.

Marcus said:
A graviton, I take it, is not something that a string theorist would impute to nature as something that actually exists----rather it is something that appears in the analysis when a flat approximation is made using Minkowski space or some other artifical convenience.
I am not sure of the beauty Lubos or others are seeing, but what is amazing to me, is that this theoretical particle assuming distinctions of quantizing gravitational wavess, could actually inhibit all those hidden dimensions.

As I have shown numerous times now, the Planck Epoch seems very real to me when we can look at the begininning and the end, and can, include this graviton in all it's features?

Time with 4d space reduced to time 3d space, and we are faced with principals that reveal "electromagnetism"{a gaussian view of hyperdimensional realities} from the unification with gravity. If this is so, then what is in seen in hyperdimensional realites of the graviton?

Laymen perspective and certainly open to corrections.

arivero said:
Well, IMHO it should be more readable if s.p.s used the conventional > quotation sign instead of bracketing everything, that is true.
Yes they are trying to control the chatter and remain pure

And yes, I went this morning to the library to get the books, I borrowed the old GSW and glanced Polchiski. I'd say that the real claim is that strings are able to quantise a 26 dim Kaluza-Klein theories or 10 dim supersym ones with very specific matter sources. This is not exactly as to quantise 4dim gravity, but well I think that 26 dim gravity is also non renormalisable, is it?
My post above yours might help, maybe not. But you have to remeber what Baez said in a link supplied by..... and I will supply quote by whom and response.[/quote]

Not my theory, but De Vries' one. Interesting anyway.
Yes most certainly.

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arivero said:
Well, IMHO it should be more readable if s.p.s used the conventional > quotation sign instead of bracketing everything, that is true.

And yes, I went this morning to the library to get the books, I borrowed the old GSW and glanced Polchiski. I'd say that the real claim is that strings are able to quantise a 26 dim Kaluza-Klein theories or 10 dim supersym ones with very specific matter sources. This is not exactly as to quantise 4dim gravity, but well I think that 26 dim gravity is also non renormalisable, is it?

Not my theory, but De Vries' one. Interesting anyway.
General relativity is non renomalizable in dimensions greater than two. But string theory has no renormalization to it at all, one of its strong points with physicists. The string graviton does not give GR (with curved space), but it gives physics that looks like GR physics, doing it in flat spacetime with exchange of particles instead of background free in a spacetime whose curvature responds to the matter and energy present.

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There is no room for such doubts, my son.

Another exquisite exchange at SPS:
Lubos says the background metric must satisfy the correct Einstein equations. then he clarifies that it does not satisfy the Einstein equations, actually, but something that is, one presumes, even more correct and furthermore that there is no room for uncertainty or doubt about this. I shall burst.

----quote----
> > [Moderator's note: Good textbooks and lectures of string theory - e.g.
> > chapters 3 of Green+Schwarz+Witten and of Polchinski - derive that
> > the background metric must satisfy the correct Einstein equations if
> > the worldsheet theory is conformal i.e. consistent.

Perhaps the language generated some of my doubts. Polchinski, pg. 112.
just says "The equation b... resembles Einstein's equation". The word
"resembles" sounds far away from a theorem. It implies that the author is
being cautious about having gravity there.

[Moderator's note: Nope. You misunderstood the word "resembles". The
reason why Polchinski uses the word "resembles" is surely not his
uncertainty about whether string theory contains gravity. There is no
room for such an uncertainty and such doubts.
The verb "resemble"
means "look like" - in other words, the equations that one derives
are not exactly the original Einstein's equations, but Einstein's
equations coupled to matter (dilaton, B-field...) which also can
acquire various new corrections. String theory also implies
what sort of matter and corrections appear, and this implication
is rigorous. The word "resemble" means that the equations are not
quite the pure and simple laws of GR from 1915. But this disagreement
does not show a flaw of string theory; on the contrary, it shows
that the simple laws of GR were not the whole story. LM]

Hmm. Do you remember where in the books is the limit of small Newton
constant?

[Moderator's note: which limit you exactly want? Linearized gravity?
In perturbative string theory, GR is obtained in the limit goes
to zero - in other words, at distances much longer than
the typical length scale associated with strings. Newton's constant
is a power of determined by dimensional analysis - times
. Sending to zero is not enough to reduce string
theory to pure GR. Even at vanishing string coupling - or, perhaps,
especially at vanishing string coupling - string theory differs from
GR or any other theory of pointlike particles. The stringy equations
of motion - for the background - are derived in Polchinski. The whole
proof is there and everyone who knows how to take limits can take them.
I am not sure what you're exactly looking for. But if you want to derive
the Newtonian limit of GR, the same proof from GR can be used in string
theory as well, as long as the distances between all objects are much
longer than where GR is a good approximation of the full
(string) theory. LM]

----end quote----

Hey Alejandro! You misunderstood the word "resembles"!

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arivero
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sps thread, remixed for PF

Before packing, I was sending a further comment to sps. I can not find the content, but here is the draft, just in case you want to follow discussion here in PF too.

=============================================
t seems that the claim is that the theory is able to execute a
consistent quantisation of Kaluza Klein theory when this theory has
a definite critical dimension and a definite content of matter
fields. This is seen as a virtue because of the uniqueness: it
fixes a very specific family of theories, say 26 dim Kaluza Klein
with the tachions or, better, the 10 dim susy version.

I am not surprised about having curvatures. It is well known that
the curvatures in Riemann tensor are essentially a set of two-dimensional
objects, so it was to be expected that a two dimensional method
as the string worldsheet were able to catch the Einstein Hilbert
action.

I was asking for a verification of the quantisation property. In
the same way that one can get classical electrodinamics from QED, one
should be able to get the classical Kaluza Klein theory in some
limit. Also I was asking because sometimes the limit process is not
the most naive; remember for instance how quantum mechanics
approaches classical mechanics in the limit of high quantum numbers,
not really in the h->0.

Well, I will be on vacation for some days, but I will carry the GSW in the backpack and a candlelight.

arivero
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Let me remark this:
LM said:
----quote from SPS moderator notes---
the background metric must satisfy the correct Einstein equations if
the worldsheet theory is conformal i.e. consistent.
IE, only the D=26 bosonic string or the D=11 susy strings do reproduce the correct Einstein equations.