As you may know, there is a lot of confusion both on the lattice and theory for the question of QCD spectrum and mostly in identification of glueballs, hybrids and other exotic states. Presently, fashion says that light unflavored mesons should be tetraquark states and this view is supported by such notable physicists as Maiani and ‘t Hooft. Now, I am living in a small volume of the available phase space of the interpretations, in good company I add, where we believe that all this very good people may be wrong about this matter. Unfortunately, this paper does not help any side of the barricade and the question is still there, open to whoever has enough good will and smartness to improve our understanding.

Regards,

Marco

today on arxiv an interesting paper on the very nature of \sigma ressonance was posted:
http://lanl.arxiv.org/abs/0910.2749
I would like to listen to your ideas on this topic!
Regards,

Rafael.

Thank you very much for the link.

Best,

Marco

Thank you. Indeed, this is a quite interesting result on a theory generally believed manageable only with perturbation techniques.

Best,

Marco

Regarding Smilga’s choice, I had this sudden flash that it might be related to a solution to a certain math problem I’ve been pursuing, which has to do with path integrals over finite configuration spaces and the like.

Given a finite group, one defines the “group algebra over the complex numbers” by using the finite group elements as a basis for a vector space with multiplication defined by the finite group multiplication rule. This defines an algebra. Wolfram.com on “Group Algebra”.

Now, given a group algebra, the stable long time propagators for individual particles correspond to the “primitive idempotents” of the algebra. Idempotent means uu = u. Primitive means that it’s not zero, and that it’s not the sum of two non zero idemopotent elements. Example, for spin-1/2, the projection operators for spin in various directions are primitive idempotents. The unit matrix is idempotent but not primitive. In a certain way, complete sets of annihilating group algebra primitive idempotents (i.e. sets where any pair multiply to zero and the sum of all of them is unity (where unity is 1 times the basis element corresponding to the identity of the finite group)) are a generalization of spinors.

Finding the primitive idempotents of a group algebra can be difficult because, with a finite group of size N, the maximum possible number of idempotents is 2^ N.

Anyway, the analogy to Smilga’s choice is that it is always possible to write down one primitive idempotent: The sum over n of g_n/N, where g_n is the basis element corresponding to the nth element of the finite group. It’s easy to show that this is a primitive idempotent.

Your question is quite interesting as are the papers you put to my attention. Let me clarify what the mapping theorem implies. You can select a set of components of a Yang-Mills field and use them to solve the corresponding equations taking them to be all equal, space-independent and being also solution of a massless quartic scalar field equation. These are Smilga solutions. Otherwise, in the most general case, the mapping is only perturbative giving

holding when the coupling g is taken large enough and being a solution of the equation for the massless quartic scalar field. As you can see, all amounts to a selection of components and so, I cannot expect that being or not in a general relativistic framework should change something. Rather, I would have serious troubles to solve exactly the corresponding equation for the scalar field. Indeed, as you know, cosmologists working with scalar fields in inflationary scenarios apply the so-called slow-roll approximation to avoid this problem. A posteriori they are able to show that this approximation is what one needs in this physical situation.

About the ghost field, I should expect a decoupling also in the most general case because this happens for algebraical reasons. This arises from the antisymmetry of the structure constants of the gauge group and so I cannot see how this field can count here. But, as you may know, the running coupling of the Yang-Mills field has a quite peculiar behavior, as I also discussed in my paper, and this means that the scenario depicted by these authors could be correct provided dark matter is cold enough to be in a kind of intermediate regime where both asymptotic freedom and the low-energy scenario fail.

Finally, let me say that a lattice analysis, using Robertson-Walker metric, could be very interesting here to see how cosmological effects enter into QCD.

Best,

Marco

please, give a look at these cosmological implications of infrared QCD propagators:

http://xxx.lanl.gov/abs/0906.2165v2
http://xxx.lanl.gov/abs/0909.2684

Are you able to formulate the gauge-to-scalar mapping also in curved backgrounds? What does this imply for ghosts (should they stay coupled as needed in aforementioned papers)?
Best,

Rafael.