I was aware of the existence of this theory since the post of Lisi in the Sabbines Hosfander "inspirational series". There he stated that "he was cooking a theory to kick the string theory ass" (or something quite similar). Not too surprisingly in the comments sectionhe was quilified by Lubos Motl as an crank.
I am not a terrible fan of group theory and this proposal of ToE (theory of everything) relies heavilly on it. Worst, it depends on E(8). Almost all my knowledge of E(8) comes from the appendix to chapter 6 of Green-Schwartz-Witten book on string theory and from the corresponding entry on wikipedia. More important than this is that it is hard to conceive that it could be possible to gain any insighth in quantum gravity by means of group theory. I mean, gravity is about diferentail geometry, maybe topology. At most it could be thought that gravity is about fibre theory with S0(3,1). Moreover, the Colleman-Mandella theorem states that it is impossible to join the gauge groups and the Lorentz group into a greater group. Everybody having studied supersymmetry knows this anyway (because supergravity scapes this no-go theorem). This is the first objection which Lubos made to the paper when he did his comment (you can read it here).
Garrett replied to that objection in a thread about his theory that is beeing discused at physics forums, concretely this . To be honest I didn´t follow this thread beyod the second page, but I am sure that a lot of information can be found there, as well as the correponding entries in the blos of Sabine Hossfander and Peter Woit (in spanish you could try the one in Migui's Forum.
With so many discusions going there I badly can say anything specially interesting. I find more encouraging the papers about the proof of the Maldacena correspondence (not conjecture any more) or one stating that type II A flux models (closelly related to some kind of braneworld scenaries) are not viable because of the lack of inflation.
So, why an entry about this topic afther all? The main reason is some blogs attacking Garrett Lisi´s not because his theory but because ¡he is a surfer!. Aparently the fact that he works teaching surf and snowboard is enoguth for this people to disqualify a theory. First, this is not the whole history. Lisi is financied by some organization named FQXI. Second, and most important, he seems to have contact with important people in the LQG community (which of course have given a warm wellcome to the theory and are wondering about intergrting it in an spin faom model). Also it is important to state that Lisis has a PhD in physics. All that is much more that Einstein had when he did his five famous contributions to physics in his "anni mirabiliies". But it is not a question of haveing "contacts". The point is that better or worst Garret has an original theory coherently presented in an standard way. Some of the ciritics of his work in the blogosfere have not some mayor contribution to physicis, and it is very unlikely that they could make something beyond very conventional and irrelevant contributions. For sure they are not going to ever make a paper which would get a tiny part of the(deserved or not) impact of lisis´s theory. If Lubos decides to say that Lisis is a crackpot he has behind him a couple of good papers in string theory, and a wonderfull blog with a lot of info in string theory (among other more questionable subjects). And he always would argue using physics (althought he can twist a bit some arguments xD). But his , imitators?, simply have not the authority to be so displicents about this questions.
Once I decided to make a post about the theory I did a quick reading of the paper. He beguins doing a brief summary about basic facts of the standard model and about lie groups theory. In that aspects it looks somehat more like a thesis article than a conventional review article. The fun of this is that it makesit accesible to a broad audiency. Afther a lot of statements relating group theory objects and particles of the standard model (and a few other which should be oberved in the future LHC is his theory is correct) he ends up with an action. The action takes the form of a BF theory, the best friend of the "spin foamers". I am surpried because I would expect gravity arising in a totally diferent way, and it makes me hard to see how unification could arise if gravity relises into this theory. But I guess that this question, and many others, would be addressed in the links that I gave about so I invite to my eventual readers to search there.
A last link, to another blogger talking about this theory. the one in U-duality. He talks about similtudes of this theory with something called homnogeneous supergravity, and possiby with topological string theory. Don't ask me why, but seems that not all string theorist are so negative about Lisi as Lubos. If I would have to give a recomendation about the paper it would be this. It seems to be an entertaining way to learn a bit about E(8), which plays an important role in some aspects of string theory.
O.K. I did this "obligatory" entry. Could you please separate that gun from my head? :P.
Jacket Distler also has finally made a post about the theory, you can read it here
I find it particularly interesting, as well as the discusion following, in which Garrett appears. Jackes identifies a weak point in the maths, and Garret agree, that if not overcomed would mean that the theory is useless, or more properly said, inconsistent, even at the classical level inwhich it is formulated. Well, as I said before, still the paper could be usefull as an introduction to E(8).