A note about AdS/CFT and Yang-Mills spectrum


There is a lot of activity about using this AdS/CFT symmetry devised in the string theory context to obtain the spectrum of a pure Yang-Mills theory in D=3+1. To have an idea about one can read here. The essential point about this approach is that it does not permit the computation of the mass gap. Rather, when given the ground state value as an input, it should be able to obtain all the spectrum. I should say that current results are indeed satisfactory and this approach is worthing further pursuing.

Apart from this, we have seen here that the ground state, as derived using the lattice computations of the gluon propagator, is quite different from current results for the spectrum as given here and here. Indeed, from the gluon propagator, fixing the QCD constant at 440 MeV, we get the ground state at 1.25. Teper et al. get 3.55(7) and Morningstar et al (that fix the constant at 410 MeV) get about 4.16(11). Morningstar et al use an anisotropic lattice and this approach has been problematic in computations for the gluon propagator ( see the works by Oliveira and Silva about) producing disagreement with all others research groups or, at best, a lot of ambiguities. In any case we note a large difference between propagator and spectrum computations for the ground state. This is a crucial point.

Experiments see f0(600) or \sigma. Propagator computations see f0(600) and \sigma but spectrum computations do not. Here there is a point to be clarified between these different computations about Yang-Mills theory. Is it a problem with lattice spacing? In any case we have a discrepancy to be understood.

Waiting for an answer to this dilemma, it would be interesting for people working on AdS/CFT to lower the input ground state assuming the one at 1.25 (better would be 1.19 but we will see this in future posts) and then checking what kind of understanding is obtained. E.g. is the state at 3.55 or 4.16 recovered? Besides, it would be nice to verify if some kind of regularity is recovered from the spectrum computed in this way.

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