I regret submitting this paper for review, now, but I will try to say what's going on.

First of all, it is based on a supposed generalization of string theory called "G-theory" which I think does not even exist. The authors have noticed that some branes in M-theory are described by Lie-3-algebras, and they have said, OK, let's consider Lie-N-algebras in general. They generalize the 3-algebra formulas in a very mechanical-looking way, and say that's the bosonic action of a Gp-brane (equation 17 forwards). Then to add fermions (top of page 7), they cite a mechanism from a paper, the full text of which I cannot find online, but whose abstract claims to explain not just confinement, but also telepathy.

As the title promises, they want to model a quark-antiquark system by a type of "BIon". BIon is not their invention, it is a kind of approximate description of an open string connecting to a D-brane, that uses Born-Infeld ("BI") electrodynamics. In "G-theory", it seems that BIons consist of wormholes between G-branes: bosonic wormholes produced by graviton exchange, and fermionic wormholes produced by gravitino exchange. The bosonic wormhole is associated with an attractive force, the fermionic wormhole with a repulsive force. The temperature dependence of these forces is calculated, and is said to plausibly describe the thermal dissociation of quarkonium.

If all this worked, it would be an audacious and imaginative paper, but I just don't believe that e.g. the various "G-brane Hamiltonians", calculated across many pages, refer to anything mathematically well-defined. Ideally that should be demonstrated by going through their argument and showing the specific omissions and non sequiturs, but for now I just have an overall impression that the discussion and analysis is far too shallow for this to be real.