Viennese physicists Harold Steinacker and Jochen Zahn completed their interesting hep-th paper
They are building on a classical solution to the Japanese IKKT matrix model. I have some trouble with that, partly because it is not a light-cone gauge description of any string theory vacuum and I don't know what all the DLCQ insights could be replaced with. But they suggest that it could work in the proper American BFSS matrix model, too.
At the end, if the construction makes any sense, it should be possible to describe the stringy vacuum informally, without a matrix model.
The matrix models may be used to derive the spectrum of the theory. Because of the reliance on matrices and blocks, the spectrum is effectively a spectrum of a braneworld. Because the matrices are finite, the individual rows and columns may be interpreted as cells of noncommutative D-branes.
So they work with the minimum nontrivial fuzzy spheres (quadruplets of D0-branes). Well, the shape may be deformed so they call them "fuzzy ellipsoids". At some brane intersections, they deduce the existence of chiral fermions – something that mildly violates some "lore" because it produces a left-right-asymmetric spectrum from the left-right-symmetric \(\NNN=4\) gauge theory of a sort. (I say "mildly" because their model isn't really a field theory at this point. It's somewhat unclear whether they claim that they know what the effective field theory really is.)
The Higgs bosons are claimed to arise naturally – to be unavoidable as some kinds of off-diagonal modes describing the fuzzy ellipsoids. There are lots of "inconvenient" extra degrees of freedom and it seems that their masses have so far no clear reasons to be vastly higher than the electroweak scale. But they hope and pray that the quantum corrections make these particles heavier which is needed to avoid contradictions with the LHC experiment.
I don't know whether the hope is substantiated. The most important reason why the authors believe that there is something about the model is that they get some Higgs fields for free, as an inevitable prediction of the scheme. Well, I am not too convinced by that because they also get lots of other unwanted particles so if you predict too many new particles, it's not too hard or nontrivial to cherry–pick the yummy ones.
At any rate, I wish them and their followers good luck. Getting realistic models from BFSS-like matrix models used to be one of my dreams that looked so "wrong" that I viewed as nearly impossible. But if that were possible, one could really see the real world as a broken phase of the maximum supersymmetry. That would be an amazing enhancement of the power of string theory and supersymmetry in the down-to-earth particle physics.