# Graviton vs gluon ball

## Main Question or Discussion Point

Can graviton possible act like gluon ball? Why not?

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mathman
Gravity (mediated by graviton - yet to be discovered) obeys an inverse square law. Strong force (mediated by gluons) is completely different. I can't see any connection. What did you have in mind?

arivero
Gold Member
An spin 2 glueball? It should be massive (this short distance).

I don't have Zee's book right here, but I think somewhere he mentions the "missing" symmetric (color) gluon as a candidate for graviton, since it would not be confined, carry an inverse distance square coupling basically to the amount of mass. This of course is just presented as an example of how one can do things wrong. Maybe that is what confuses the OP ?

I imagine Zee is talking about the

$$| \bar{r}r \rangle + | \bar{g}g \rangle + | \bar{b}b \rangle$$

combination of gluons (which is the trivial representation of SU(3))? This reason this cannot be the graviton is because it would couple to all baryons with the same strength (since all baryons are colourless), and yet baryons have different mass and should couple differently to the graviton.

Since there is an allowed 3 gluon vertex and 4 gluon vertex in QCD, we can in principle have a bound state of gluons.

I have yet to see the Lagrangian for a QFT of gravity, so I can't comment about the allowed vertices, and indeed the possibility of a bound state.

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This reason this cannot be the graviton is because it would couple to all baryons with the same strength (since all baryons are colourless), and yet baryons have different mass and should couple differently to the graviton.
This is not obvious. One can argue that "there are more gluons in a more massive hadrons". Anyway, the idea has yet other caveats.
Since there is an allowed 3 gluon vertex and 4 gluon vertex in QCD, we can in principle have a bound state of gluons.
This also is not obvious at all ! Despites extensive searches (to which I participate, I am not saying this is worthless), we have only very indirects mixing hints in only a few mesons (not even to mention pure glueballs). Besides, it is sometimes dangerous to jump to the conclusion "because something is not forbidden, it must be realized in Nature". Not all models of confinements agree on the possibility of free glueballs. The presence of light quarks, either in the valence or only in the (virtual) sea, is sometimes believed to be essential.

Can graviton possible act like gluon ball? Why not?

Affirmative, by setting their fine structure constants to equivalence:

Gravitational fine structure constant equivalent to strong fine structure constant:
$$\boxed{\alpha_g = \alpha_s}$$

Affirmative, by setting their fine structure constants to equivalence:

Gravitational fine structure constant equivalent to strong fine structure constant:
$$\boxed{\alpha_g = \alpha_s}$$
No, as indicated by arivero the graviton has spin-2 (couples to the EMT). The gluon has spin-1 (vector).

arivero
Gold Member
On other hand, if you only want to mimic attractiveness of like charges, then a spin 0 glueball could do the trick (again ,were it massless). Probably it would fail to predict the orbit of Mercury.

EMT = Energy Momentum Tensor

Pure massless gluons and pure massless graviton 'balls' probably cannot exist within the framework of QCD and QGD, both are required to couple between masses as bosonic force carriers.

However, I would still defend gluon-gravitational Grand Unification for a degenerate QCD QGP plasma (ball), which was my original presumption for a 'gluon ball'.

Gravitational fine structure constant equivalent to strong fine structure constant:
$$\boxed{\alpha_g = \alpha_s}$$

Degenerate Grand Unification QCD-QGD QGP mass:
$$m_g = \sqrt{\frac{\hbar c \alpha_s(m_Z)}{G}}$$

$$\boxed{m_g = 7.46426018425756 \cdot 10^{- 9} \; \text{kg}}$$
$$\boxed{E_g = 4.18714467091867 \cdot 10^{18} \; \text{GeV}}$$

Reference:
http://en.wikipedia.org/wiki/Quark-gluon_plasma" [Broken]

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However, I would still defend gluon-gravitational Grand Unification for a degenerate QCD QGP plasma (ball), which was my original presumption for a 'gluon ball'.
Ah but that is very interesting ! It was not clear from the beginning of the discussion anybody was interested into the AdS/CFT correspondence and the so-called "RHIC fireball". As far as I am aware, the first serious (courageous) attempt in this direction was The RHIC fireball as a dual black hole. This line has been very productive. A recent review can be found in Introduction to String Theory and Gauge/Gravity duality for students in QCD and QGP phenomenology.

On other hand, if you only want to mimic attractiveness of like charges, then a spin 0 glueball could do the trick (again ,were it massless).
I don't want to hack this thread but... I'll do it anyway :tongue2:
How would you write down a lagrangian involving only a scalar field, supposed to be the most relevant component of the graviton field in a certain low energy/long distance limit, while keeping non-abelian effects ?
I was thinking to try someything like
$$S=\int d^4x \left[\partial h\partial h+\sqrt{G}h\partial h\partial h+Gh^2\partial h\partial h+\cdots + \sqrt{G}hT \right]$$
by directly replacing in the usual expansion the graviton with a scalar field. Do I make sens ? :uhh:

The lagrangian density for a massless spin-two field:
$$\mathcal{L} = - \frac{1}{2} \partial_{\lambda} h_{\mu \nu} \partial^{\lambda} h^{\mu \nu} + \partial_{\lambda} h_{\mu}^{\lambda} \partial_{\nu} h^{\mu \nu} - \partial_{\mu} h^{\mu \nu} \partial_{\nu} h + \frac{1}{2} \partial_{\lambda} h \partial^{\lambda} h$$

Einstein gravity weak field limit:
$$h \equiv h_{\mu}^{\mu}$$

Scalar field theory:
$$\mathcal{S}=\int \mathrm{d}^{D-1}x \, \mathrm{d}t \mathcal{L}$$

Solution for a scalar field lagrangian density massless spin-two field:
$$\boxed{\mathcal{S}=\int \mathrm{d}^{D-1}x \, \mathrm{d}t \left[ - \frac{1}{2} \partial_{\lambda} h_{\mu \nu} \partial^{\lambda} h^{\mu \nu} + \partial_{\lambda} h_{\mu}^{\lambda} \partial_{\nu} h^{\mu \nu} - \partial_{\mu} h^{\mu \nu} \partial_{\nu} h + \frac{1}{2} \partial_{\lambda} h \partial^{\lambda} h \right]}$$

Tensor scalar theory solution: ???
$$\boxed{T^{\mu\nu}_g = \frac{c^4}{8 \pi G} \left[ - \frac{1}{2} \partial_{\lambda} h_{\mu \nu} \partial^{\lambda} h^{\mu \nu} + \partial_{\lambda} h_{\mu}^{\lambda} \partial_{\nu} h^{\mu \nu} - \partial_{\mu} h^{\mu \nu} \partial_{\nu} h + \frac{1}{2} \partial_{\lambda} h \partial^{\lambda} h \right]}}$$

Reference:
http://en.wikipedia.org/wiki/Scalar_field_theory" [Broken]
http://arxiv.org/PS_cache/gr-qc/pdf/0212/0212113v2.pdf" [Broken]
http://en.wikipedia.org/wiki/Scalar_theories_of_gravitation" [Broken]

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blechman
I don't want to hack this thread but... I'll do it anyway :tongue2:
How would you write down a lagrangian involving only a scalar field, supposed to be the most relevant component of the graviton field in a certain low energy/long distance limit, while keeping non-abelian effects ?
I was thinking to try someything like
$$S=\int d^4x \left[\partial h\partial h+\sqrt{G}h\partial h\partial h+Gh^2\partial h\partial h+\cdots + \sqrt{G}hT \right]$$
by directly replacing in the usual expansion the graviton with a scalar field. Do I make sens ? :uhh:
Unfortunately, I don't think this works - I remember playing with this idea in grad school, and we found that we can always kill such "nonabelian" terms with a (nonlinear) field redefinition. VERY sketchily:

$$S = \int d^4x Z(\phi)(\partial\phi)^2$$

Let $\phi' = \phi/\sqrt{Z(\phi)}$. So at the end of the day, we end up with a free scalar field!

You have to be a little careful with this since the Path Integral measure can also change, but I think the result is still rigorous. Check out Tomas Ortin's textbook "Gravity and Strings" - it talks about these kinds of theories.

We can have 4-derivative terms, but these are a problem - they introduce ghosts and other nasties. And besides, they wouldn't correspond to the usual "scalar-Einstein-Hilbert action".

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Hmm I'm in high school. So I don't get the math. Can anyone explain the concepts?

we found that we can always kill such "nonabelian" terms with a (nonlinear) field redefinition
Thank you for you answer I will keep playing with it and try to redefine my field to "gauge" away my non-abelian terms. Intuitively, it does seem odd because any non-abelian group acting on my scalar could only do so trivially. I expected this to be fishy actually.
Check out Tomas Ortin's textbook "Gravity and Strings" - it talks about these kinds of theories.
Arg, I just bought Kiefer's books and barely began it So little time...

blechman
Thank you for you answer I will keep playing with it and try to redefine my field to "gauge" away my non-abelian terms. Intuitively, it does seem odd because any non-abelian group acting on my scalar could only do so trivially. I expected this to be fishy actually.
it's NOT a "gauge" issue - it's a field redefinition. quite different. there's no symmetry argument, it's just that these nonlinear terms can all go into a sort-of wave-function renormalization constant, and are therefore irrelevant; that is: they don't lead to any physical observables. the "Z" I mention is NOT a transformation.

A similar argument fails for the usual graviton due to the tensor nature of the interactions - you cannot "reabsorb" the nonlinear terms in that case. Scalar fields are a little bit TOO trivial.

Arg, I just bought Kiefer's books and barely began it So little time...
yeah, there's a lot to read out there. Have fun!

Ortin does explain scalar gravity theories very well, including why they fail (wrong precession of mercury; no bending of light,...). This is, of course, not to be confused with Brans-Dicke-Jordan theory, where there is BOTH scalar AND tensor.

Haelfix
Just glancing at it briefly, I think there is a topological term in one of those nonlinear bits which is why it doesn't work and can be redefined away.

I could be wrong though.

blechman
Hmm I'm in high school. So I don't get the math. Can anyone explain the concepts?
Hi Bright Wang.
I'm sorry to say this thread has been hijacked! I don't think I can explain the concepts without a LOT of time and several blackboards, but the quick no-math summary is like this:

you asked about gluballs and gravitons. From my point of view: glueballs cannot be gravitons for a number of reasons - they're massive, first of all, and the graviton is supposed to be massless; they interact with the STRONG nuclear force (note emphasis on strong!) while gravity is weak - in fact, it's super-super-super-SUPER-SSSUUUPPPEEERRR!!!!!!! weak!

Then people started talking about the "singlet gluon", which is a possible particle that could come out of the theory of strong nuclear force (called "Quantum ChromoDynamics", or QCD). This particle does not seem to exist in nature (and there are plenty of satisfying explanations out there for why this is so), but if it did, it would interact weakly and be massless. HOWEVER, it would have the wrong spin (a quantum mechanical angular momentum) - in particular, it would have spin angular momentum $\hbar$ while the graviton should have spin angular momentum $2\hbar$ - that's a very important factor of 2! In case you don't know $\hbar\sim 10^{-34}$ Joules-seconds is Planck's constant - it has units of angular momentum.

Then the thread started to go awry from your point of view! people started (wisely!) asking about ways to modify Einstein's theory of general relativity to get some interesting results. This is where the friendly explanations must stop, I'm afraid, as things start to get more technical.

I hope that quick and sloppy summary helps you understand what happened. Last edited:
it's NOT a "gauge" issue - it's a field redefinition. quite different. there's no symmetry argument, it's just that these nonlinear terms can all go into a sort-of wave-function renormalization constant, and are therefore irrelevant; that is: they don't lead to any physical observables. the "Z" I mention is NOT a transformation.
Yes, that's why I put "gauge" and not gauge Thanks for the correction though.

blechman
Yes, that's why I put "gauge" and not gauge Thanks for the correction though.
it is an important distinction, though! you mention wondering how this could be since:

"any non-abelian group acting on my scalar could only do so trivially."
But this is not the issue here.

Oh hmm I never asked if Gluon and graviton are the same. It was meant that if its possible for graviton to have the "Ball" properties and as in it interact with it self.

blechman
Oh hmm I never asked if Gluon and graviton are the same. It was meant that if its possible for graviton to have the "Ball" properties and as in it interact with it self.

there are two things: gluons and glueballs (bound states of gluons + quantum sea of quark-antiquark pairs). normal gluons certainly can't be graviton (they're strong nuclear). glueballs cannot either, because, as was said previously, they're massive (bad!) and strongly interacting (also bad!). actually, the statement that they're massive is still an open question, but most of the particle-physics community would agree that they are (\$1M if you can prove it mathematically - Clay Math Problem).

I know that you weren't initially talking about gluons, but it then came up that there might also be the "singlet gluon", but this cannot be the graviton since (among other problems) it is spin-1.

if you are asking if the graviton can be some sort of composite object LIKE a glueball (not made of gluons but some as yet undescovered thing), that's yet another interesting question. This is loaded with lots of problems, but people are interested in it and trying to come up with ways to fix said problems.

Haelfix