The title of the 7 May talk was just posted today. http://relativity.phys.lsu.edu/ilqgs/schedulesp13.html Code (Text): [U]ILQGS Spring 2013 Schedule[/U] DATE Seminar Title Speaker Institution Jan 29 [B]Entanglement in loop quantum gravity[/B] Eugenio Bianchi Perimeter Institute Feb 12 [B]Dynamical chaos and the volume gap [/B] Hal Haggard CPT Marseille Feb 26 [B]Gravity electroweak unification[/B] Stephon Alexander Haverford College Mar 12 [B]Quantum reduced loop gravity[/B] E.Alesci/F.Cianfrani Univ. Erlangen Mar 26 [B]Bianchi I LQC[/B] Brajesh Gupt LSU Apr 9 TBA Karim Noui Univ Tours Apr 23 TBA Martin Bojowald Penn State May 7 [B]Emergence of BF theories and gravi-weak Plebanski models from spinors[/B] Antonino Marciano Dartmouth College Marciano's talk will be about this paper: http://arxiv.org/abs/1212.5246 Gravitational origin of the weak interaction's chirality Stephon Alexander, Antonino Marciano, Lee Smolin (Submitted on 20 Dec 2012) We present a new unification of the electro-weak and gravitational interactions based on the joining the weak SU(2) gauge fields with the left handed part of the space-time connection, into a single gauge field valued in the complexification of the local Lorentz group. Hence, the weak interactions emerge as the right handed chiral half of the space-time connection, which explains the chirality of the weak interaction. This is possible, because, as shown by Plebanski, Ashtekar, and others, the other chiral half of the space-time connection is enough to code the dynamics of the gravitational degrees of freedom. This unification is achieved within an extension of the Plebanski action previously proposed by one of us. The theory has two phases. A parity symmetric phase yields, as shown by Speziale, a bi-metric theory with eight degrees of freedom: the massless graviton, a massive spin two field and a scalar ghost. Because of the latter this phase is unstable. Parity is broken in a stable phase where the eight degrees of freedom arrange themselves as the massless graviton coupled to an SU(2) triplet of chirally coupled Yang-Mills fields. It is also shown that under this breaking a Dirac fermion expresses itself as a chiral neutrino paired with a scalar field with the quantum numbers of the Higgs. 21 pages
It's interesting that out of the 8 ILQGS talks scheduled for this Spring semester, TWO of them are about gravi-weak unification. And both of those talks stem from the paper mentioned in the previous post. One talk, by Stephon Alexander, is coming up just this month: Feb 26 Gravity electroweak unification The other, by Antonino Marciano, was just posted on the schedule today, and is further off: May 7 Emergence of BF theories and gravi-weak Plebanski models from spinors
I just looked back at the 4th quarter 2012 MIP poll https://www.physicsforums.com/showthread.php?t=661347 and noticed that the person who spotted the Alexander et al paper on Gravity Electroweak Unification as important was Atyy. I was feeling cautious about it at the time--it is clearly important if the unification they propose has a chance of working and a real possibility of being right. But it was too much of a stretch for me to consider that, and must have also been for several other people. Atyy was the only one who ventured to bet on it. Now I see that Jorge Pullin, who organizes the ILQGS, has devoted 2 out of this Spring semester's 8 talks to G-E unification. It looks like he is betting on it being at least a worthwhile thing to study. So hat-tip to Atyy on this one. People trust Pullin's knowledge of the QG field and his "horse-sense"---he is regularly asked to organize and chair QG sessions of conferences. So there could be something to this. BTW in the December 2012 G-E unification paper http://arxiv.org/abs/1212.5246 the author's referred to a followup they had in preparation. So I suppose that second paper, which has not yet appeared on arxiv, could be the subject of the second ILQGS talk (by Marciano in May)
Stephon Alexander is a theoretical physicist now mostly associated with Ivy League institutions. When I first knew of him he was at Stanford SLAC, then at Penn State and Haverford, and now holds a faculty position at Dartmouth. (This is from memory, I haven't checked his Bio). His 31 published papers have garnered 1198 for an average of 38.6 citations each: http://inspirehep.net/author/S.Alexander.2/ (corrected) The research gambit he will be presenting 12 days from now at ILQGS is unusual. So far there has just been one paper on it. Also unusual is the fact that his Dartmouth postdoc Marciano, one of his co-authors on the paper, will be giving a second talk at ILQGS on the same research a few weeks later. So as to have them handy, here are links to the abstract, which I quoted in post #1 above. http://arxiv.org/abs/1212.5246 http://inspirehep.net/record/1208288?ln=en Gravitational origin of the weak interaction's chirality Stephon Alexander, Antonino Marciano, Lee Smolin (Submitted on 20 Dec 2012, last revised 7 Jan 2013) The INSPIRE database assigns keywords automatically and this is what the system came up with for this paper: | graviton: massless | gravitation: coupling | gauge field theory: SU(2) | gravitation: interaction | graviton: coupling | neutrino: chiral | stability: phase | field theory: scalar | coupling: Yang-Mills | action: Plebanski | group: Lorentz | fermion: Dirac | triplet: SU(2) | ghost: scalar | spin: 2 | weak interaction | space-time | parity | quantum number | right-handed | left-handed There's more biographical detail in the Dartmouth news article: http://now.dartmouth.edu/2012/03/th...nder-to-join-dartmouth-as-e-e-just-professor/ The ILQGS page where Stephon's slides and audio of his 26 February talk will be posted is: http://relativity.phys.lsu.edu/ilqgs/ Sometimes the slides PDF is posted a day or so in advance which can be a big help in understanding the talk.
In a little over a week, Alexander will be giving a talk online, where he describes a way to unify gravity with the standard model. This is a dark horse proposal that seems suddenly to have appeared out of nowhere, and which might be right. Because it is not only a quantum gravity theory, but involves the electroweak sector of the Standard Model, it is TESTABLE---indeed probably testable at LHC design energies. So this is something that we haven't heard about which conceivably could be on trial when LHC is restarted in a couple of years from now. The theory gives rise to one or more Dark Matter candidates. Personally I'd like to be prepared to understand some of Alexander's talk next Tuesday, so I'm taking a look at the paper it will be based on. +++++++++++++++++++++++ In the introduction they review 3 main obstacles that have stood in the way of unifying gravity with particle theory: ==quote page 1== The ambition of unifying gravity with the other interactions faces three big obstacles: 1. Gravity is described by a dynamical metric while the other interactions are described by connection fields. Consequently the Einstein action is linear in curvature while the Yang-Mills action is quadratic in gauge field strength. 2. The standard model can be quantized perturbatively, because its action is a polynomial of dimension four terms, while the Einstein-Hilbert action, being non-polynomial, is challenging to quantize. 3. The standard model of particle physics is chiral, while gravity, at least at the classical level, is not. Any unification must explain why parity is broken only for the weak interactions. The first two challenges are addressed by the Ashtekar-Plebanski formulations of general relativity in which gravity is described by a gauge field [1, 2], while the metric is emergent [3, 4]. These connection formulations of gravity are drastically simpler than Einstein’s original metric formulation, as the action and hamiltonian formulations are based on cubic polynomials in the basic fields, which is a much better situation for quantization than Einstein’s non-polynomial formulation. Indeed these theories are as simple as non-linear theories can be, with purely quadratic field equations. Remarkably, these connection formulations of gravity address the issue of chirality as well... ==endquote== The paper that we have, which came out two months ago (20 December) was mainly concerned with the issue of chirality. Things may have progressed and broadened in the intervening two months since the paper appeared: the title of next Tuesday's talk by Alexander is Gravity Electroweak Unification.
The conclusions section on page 14 summarizes what's going on here: ==quote http://arxiv.org/abs/1212.5246 == 8 Conclusion Ever since the discovery and experimental success of the standard electroweak theory, the origin of the weak interaction’s chirality has remained a mystery. In this work we we have reached the conclusion that a parity symmetric theory of gravity holds the key to the chiral origin and maximal parity violation of the weak interaction. In particular, we describe a parity symmetric theory of gravity that has a symmetry broken phase, which organizes the degrees of freedom to give rise to general relativity coupled to a SU(2) Yang-Mills theory. The emergence of gravity and the weak interaction is made possible because gravity has been shown to be completely described in terms of purely left-handed variables [9]. This leaves the right handed connection to function as the weak interaction connection. ==endquote==
How do the authors explain how they get around the Coleman–Mandula theorem? In the 1967 paper this reads "We prove a new theorem on the impossibility of combining space-time and internal symmetries in any but a trivial way." It is often stated that super symmetry is the only known "loop-hole". Not an expert on this, wonder what the explanation is.
Hi Julian! I should quote this short paragraph from page 4 about spontaneous symmetry breaking (SSB) in theories involving gravity: ===quote page 4 from AMS paper http://arxiv.org/abs/1212.5246 === The phenomena of spontaneous gravitational symmetry breaking were discussed earlier in [11] where it was shown that an extended Plebanski action of the form of (2), for a gauge group G which contains the Lorentz group, SO(3,1), suffers spontaneous symmetry breaking to an Einstein-Yang-Mills theory with a Yang-Mills gauge group in G/SO(3, 1). The same phenomena were demonstrated by Torres-Gomez and Krasnov for the chiral SU(2)_{L }subgroup of the Lorentz group [15]. Krasnov also had earlier origi- nated the notion of extending the Plebanski action in [16], with G taken to be the chiral left handed space-time connection valued in SU(2)_{L}. He has also explored a closely re- lated set of theories whose actions are purely functions of connections, and demonstrated the phenomena of gravitational spontaneous symmetry breaking there [17]. ==endquote== The paper [11] where gravitational SSB was discussed is http://arxiv.org/abs/0712.0977 and I think I'll have a look at that before going further. They also mention two recent papers by Krasnov [17] where gravitational SSB is also discussed. Those two would be: Spontaneous symmetry breaking and gravity, http://arxiv.org/abs/1112.5097 A Gauge Theoretic Approach to Gravity, http://arxiv.org/abs/1202.6183 BTW if I recall correctly, the late Sidney Coleman was Lee Smolin's thesis advisor at Harvard. == from the introduction of 0712.0977 == We close the introduction by noting that the well-known Coleman-Mandula no-go theorem[19] is avoided because that only applies to an S-Matrix whose symmetries include global Poincare invariance. This theory, like general relativity, has no global symmetries, the Poincare symmetry acts only on the ground state not the action, and only in the limit in which the cosmological constant is zero. In fact, there is a nonzero cosmological constant, as it is related to parameters of the theory. By the time the S matrix in Minkowski spacetime could be defined in this theory one will be studying only small perturbations of a ground state in a certain limit and the symmetry will only apply in that limit and approximation. As we shall see below, the symmetry will already be broken by the time that approximation and limit are defined, in such a way that Coleman-Mandula theorem could be satisfied in its domain of applicability. ==endquote== Interesting stuff! I also want to have a look at the two papers by Kirill Krasnov. He is listed as one of the invited speakers at this years Loops conference, which will be held at Perimeter in July. That could be interesting too.
In http://arxiv.org/abs/0712.0977 Smolin says: "We close the introduction by noting that the well-known Coleman-Mandula no-go theorem[19] is avoided because that only applies to an S-Matrix whose symmetries include global Poincare invariance. This theory, like general relativity, has no global symmetries, the Poincare symmetry acts only on the ground state not the action, and only in the limit in which the cosmological constant is zero." and in the same paragraph hes says: "By the time the S matrix in Minkowski spacetime could be defined in this theory one will be studying only small perturbations of a ground state in a certain limit and the symmetry will only apply in that limit and approximation. As we shall see below, the symmetry will already be broken by the time that approximation and limit are defined, in such a way that Coleman-Mandula theorem could be satisfied in its domain of applicability." I think I need to think about this more...
I see we were, unbeknownst to each other, quoting the same passage from that 2007 paper We should keep an eye on the list of invited speakers at the July Loops 13 conference: http://www.perimeterinstitute.ca/conferences/loops-13 So far there are just 11 names on the list, and Kirill Krasnov is one. I expect more names will be added over the next month or two. I would not be surprised if Stephon Alexander is one of the speakers. This whole business of unifying gravity and electroweak interactions seems potentially quite important.
I was so engrossed in this passage from the paper you referred to that I didn't notice you had quoted this passage as well.
I'm probably more to blame for not noticing but why shouldn't we quote the same passage if we feel like it?! No harm done. It's an important highly relevant excerpt from the paper.
Great talk by Stephon!!! You have to check this out! http://pirsa.org/12100116 what this gets you is a video for 5 or so short talks from October 2012, where Stephon starts around minute 18 and goes to about minute 34. So you have to drag the button to minute 18 (more exactly 18:40) in order to skip the first of the short talks and get to the start of Stephon's. The whole video is 95 minutes and the abstract (TOC) says that Lee is also talking about Gravity and Weak Interactions---basically giving a continuation of what Stephon Alexander starts----parts I and II of the same talk. Lee Smolin's part comes right after---starting around minute 35. He talks only to minute 52 but then gets a ton of questions (good ones!) and the whole segment lasts to minute 63. The whole segment, parts I and II, with Q&A, is pretty exciting. I think Roberto Percacci is there, and asks a question. There are a bunch of Asym Safe QG people at the conference. BTW Stephon is a really good speaker. It's an impressively well-organized brief lecture. This is a good preparation for his ILQGS talk coming up in one week on Tuesday 26 Feb. Interestingly---I did not anticipate how close to Lqg this Gravity-Weak unification approach is---Lee showed a significant overlap. This approach uses the Ashtekar SU(2) connection formalism and is basically non-perturbative---there is no fixed background geometry. I suppose at some point spin foam and lattice gauge QFT blend---a spin foam is a background independent kind of lattice---and the different formalisms are no longer so distinct. Not sure about this but I caught this suggestion in both parts of the talk.
Julian, and anyone else that might be reading, the Alexander, Marciano, Smolin paper is one of the (underappreciated) candidates on the most recent poll: https://www.physicsforums.com/showthread.php?t=661347 If you think the paper is especially interesting (which I certainly do!) you might want to consider checking the poll out and possibly responding. The poll is multi-choice and remains open to anyone who has not yet voted. At the time of posting the poll (end December) I overlooked the considerable potential significance of this paper, as I believe many of the rest of us did.
Actually that's why I voted for it. Apparently, it is problematic to put chiral interactions on the lattice. So I'm wondering if they can help solve the problem. http://arxiv.org/abs/0912.2560:"there is currently no practical way to regulate general nonabelian chiral gauge theories on the lattice." " http://arxiv.org/abs/1003.5896:"we do not yet have a method of approximating an arbitrary chiral gauge theory by latticizing and then simulating it on a computer even in principle." Also in Wen's manifesto http://dao.mit.edu/~wen/talks/06TDLee.pdf (last slide), he says: "Seven mysteries/wonders of universe: (1) Identical particles (2) Fermi statistics (3) Tiny masses of fermions (proton mass ~ 10^{-20} Planck mass) (4) Chiral fermions (5) Gauge interactions (6) Lorentz invariance (7) Gravity Starting from lattice bosons/spins, we can explain 4 of seven: Identical particles, Fermi statistics, Gauge interactions, Small masses, and, may be even Gravity. Parity violation and chiral fermions carry a deep message, I believe, from the Planck scale. 50 years after its discovery, we still do not know how to decode it. Parity violation and chiral fermions, like a light house in dark ocean, will guide us to sail into unknown territory."
Gravity+matter unification talk online in five days---Tuesday 26 April. The links to audio and to slides PDF will be posted here: http://relativity.phys.lsu.edu/ilqgs/ The title of the talk is Gravity Electroweak Unification The speaker is Stephon Alexander, a professor of physics at Dartmouth. The paper to read, to prepare for the talk is: http://arxiv.org/abs/1212.5246 Gravitational origin of the weak interaction's chirality Stephon Alexander, Antonino Marciano, Lee Smolin (Submitted on 20 Dec 2012) We present a new unification of the electro-weak and gravitational interactions based on the joining the weak SU(2) gauge fields with the left handed part of the space-time connection, into a single gauge field valued in the complexification of the local Lorentz group. Hence, the weak interactions emerge as the right handed chiral half of the space-time connection, which explains the chirality of the weak interaction. This is possible, because, as shown by Plebanski, Ashtekar, and others, the other chiral half of the space-time connection is enough to code the dynamics of the gravitational degrees of freedom. This unification is achieved within an extension of the Plebanski action previously proposed by one of us. The theory has two phases. A parity symmetric phase yields, as shown by Speziale, a bi-metric theory with eight degrees of freedom: the massless graviton, a massive spin two field and a scalar ghost. Because of the latter this phase is unstable. Parity is broken in a stable phase where the eight degrees of freedom arrange themselves as the massless graviton coupled to an SU(2) triplet of chirally coupled Yang-Mills fields. It is also shown that under this breaking a Dirac fermion expresses itself as a chiral neutrino paired with a scalar field with the quantum numbers of the Higgs. 21 pages Video of two previous talks on this topic (by Alexander and by Smolin) begins at minute 18 of this PIRSA resource: http://pirsa.org/12100116 Quantum Gravity and the Weak Interactions (Recorded in October 2012) Alexander's talk begins shortly after minute 18. Smolin's talk comes immediately after that and begins around minute 35. Alexander's online ILQGS talk next week will be followed up later this Spring by a second ILQGS talk, by Marciano, on the emergence of gravi-weak Plebanski models from spinors. The Plebanski action for General Relativity is obviously the basis for this whole development (that plus the Ashtekar connection formalism). So we should know who Jerzy Plebanski (1928-2005) was. He proposed this action for GR in 1977 [19] J.F. Plebanski. On the separation of einsteinian substructures. J. Math. Phys., 18:2511, 1977. As far as I know, the first Spin Foam quantization of the Plebanski action was given by Perez in 2002: http://arxiv.org/abs/gr-qc/0203058 Spin foam quantization of SO(4) Plebanski's action Alejandro Perez (Submitted on 15 Mar 2002) Adv.Theor.Math.Phys. 5 (2002) 947-968 Obviously if electroweak interactions can be captured by an extension of the Plebanski action that would be one approach to unifying quantum geometry and matter.
Some elementary comments that I wanted to make about the paper by Alexander et al. First, the headline idea of the paper seems to be a new twist on the general idea of "gravity as a gauge theory" - not in the stringy sense of AdS/CFT, with gravity being dual to a gauge theory in one less dimension, but in the LQG sense of using Ashtekar variables and then quantizing them in a different way to ordinary QFT. There have of course been long debates about the viability of the latter way of proceeding, and I don't want to repeat them here, I just want to state that the paper falls into that contested domain. (If I'm missing something and it doesn't, could someone please point this out.) Second, the following part really has problems ... ... because it sort of glides past the difference between being a fermion and being a boson! I don't know what the authors are thinking here. Are they hoping that this is where the Higgs actually comes from, and just not mentioning the problem that it needs to be a boson? edit: I didn't make my first point too well. I don't want to start another round of general debate about LQG, but there are ways in which the general issues of LQG interact with the specifics of this paper. I'll make a follow-up comment shortly.
Hi Mitchell, I think by "glide past" you must be referring to the highlighted part of this introductory summary on page 6. Please correct me if I'm wrong. ==quote 1212.5246 page 6== To summarize, we make four physical hypotheses: ￼ • The SU(2) of the weak interactions is unified with the chiral representation of grav- ity in a single SL(2, C) connection. This was proposed earlier by Alexander [24] and by Nesti and Percacci [25]. A toy-model in 3D was presented in [26] by Alexander, Marciano` and Tacchi, together with its spin-foam quantization. • The chirality of the standard model arises from a spontaneous breaking of parity in the gravitational dynamics. It is the weak interactions that break parity because the weak SU(2) gauge connection is in fact a chiral half of what is originally the space-time connection. • This mechanism also explains why parity is maximally violated in the weak inter- actions. The parity mirror of the coupling of weak isospin to matter is the coupling of the left handed part of the space-time connection to left-handed spinors. • Under the symmetry breaking, right handed space-time spinors become internal isospinors. More specifically, consider the Higgs field, a space-time scalar valued in the 1/2 of gauged isospin and the sterile neutrino (or right handed neutrinos in general) which are isospin singlets but space-time spinors. These are mirrors of each other under the parity symmetry that exchanges the SU(2)_{L} and SU(2)_{R} parts of the original connection, and are hence unified in a single Dirac spinor. The basic dynamics of the SL(2,C)_{C} extended Plebanski action are detailed in the next section... ==endquote== Let me know if you were referring to some different passage. I think they return to this, and give additional detail on pages 13 and 14, equations (62) through (66). That is where you might find that they do not "glide" so much, but give more of the nitty-gritty. It seems there is a symmetry-unbroken phase, where the two fields combine to form a Dirac spinor. And on the other hand a symmetry-broken phase where they do not combine in that fashion, but give two separate things which are possibly of interest. I don't know if you have already looked at that section, called Matter couplings, which is towards the end of the paper, right before Conclusions.
It was hard deciding what to say here. My inner Lubos, whose opinions I respect, says that http://arxiv.org/abs/1212.5246 is a bad paper. All their manipulations are either formal or classical, they never construct the quantum theory, so they never face the problems of treating gravity as a gauge theory (lack of a semiclassical limit, abnormal method of quantization, infinite undetermined couplings of spin foams) or the problems of their proposed spinorial unification (how can a boson, the Higgs, be related by parity to a fermion, the sterile neutrino?). But my inner Lubos doesn't have the knowledge of the real Lubos, and the debates about loop gravity get pretty technical. Loop-inspired research is diverse enough that most of it could be wrong and still someone might have a good idea about quantum geometry; and I am engaged elsewhere in "wishful thinking" of my own, i.e. theoretical speculations that I don't even know to be mathematically well-defined; so I could keep my opinions to myself and say, live and let live. However, this paper can be viewed from another angle where I have more of an open mind. This is the possibility that the use of the Plebanski action in loop gravity might have some crossover with new twistor gravity. I mentioned this in the "twistor networks" thread, and it turns out that Lionel Mason suggested this at Zakopane in 2010 - see the last slide of his talk. If you look at slide 33, you will see where I think there's an opening for "chiral graviweak unification" to enter - the division of that action into two parts. So for me that's the interesting question now - if you express the graviweak ideas of Nesti & Percacci, etc., in twistorial variables, how closely do they resemble Mason's division of a twistor action into "anti-self-dual" and "maximum-helicity-violating" parts? And this is something I have not yet tried to answer, at this point it's pure intuition and could be thoroughly misguided.
Since we turned a page I will bring forward the main links to what we're discussing in this thread. There's an online gravity+matter unification talk Tuesday 26 April. The links to audio and to slides PDF will be posted here: http://relativity.phys.lsu.edu/ilqgs/ The title of the talk is Gravity Electroweak Unification The speaker is Stephon Alexander, a professor of physics at Dartmouth. The paper to read, to prepare for the talk is: http://arxiv.org/abs/1212.5246 Gravitational origin of the weak interaction's chirality Stephon Alexander, Antonino Marciano, Lee Smolin (Submitted on 20 Dec 2012) We present a new unification of the electro-weak and gravitational interactions based on the joining the weak SU(2) gauge fields with the left handed part of the space-time connection, into a single gauge field valued in the complexification of the local Lorentz group. Hence, the weak interactions emerge as the right handed chiral half of the space-time connection, which explains the chirality of the weak interaction. This is possible, because, as shown by Plebanski, Ashtekar, and others, the other chiral half of the space-time connection is enough to code the dynamics of the gravitational degrees of freedom. This unification is achieved within an extension of the Plebanski action previously proposed by one of us. The theory has two phases. A parity symmetric phase yields, as shown by Speziale, a bi-metric theory with eight degrees of freedom: the massless graviton, a massive spin two field and a scalar ghost. Because of the latter this phase is unstable. Parity is broken in a stable phase where the eight degrees of freedom arrange themselves as the massless graviton coupled to an SU(2) triplet of chirally coupled Yang-Mills fields. It is also shown that under this breaking a Dirac fermion expresses itself as a chiral neutrino paired with a scalar field with the quantum numbers of the Higgs. 21 pages Video of two previous talks on this topic (by Alexander and by Smolin) begins at minute 18 of this PIRSA resource: http://pirsa.org/12100116 Quantum Gravity and the Weak Interactions (Recorded in October 2012) Alexander's talk begins shortly after minute 18. Smolin's talk comes immediately after that and begins around minute 35. Alexander's online ILQGS talk next week will be followed up later this Spring by a second ILQGS talk, by Marciano, on the emergence of gravi-weak Plebanski models from spinors. The Plebanski action for General Relativity is obviously the basis for this whole development (that plus the Ashtekar connection formalism). So we should know who Jerzy Plebanski (1928-2005) was. He proposed this action for GR in 1977 [19] J.F. Plebanski. On the separation of einsteinian substructures. J. Math. Phys., 18:2511, 1977. AFAICS the above paper and talks are not directly concerned with quantum gravity. The work here is carried out on a classical level. The Plebanski action is a formulation of classical GR (where the variable is a connection rather than a metric) and the idea here is to extend the Plebanski action to include some types of matter interaction. What mathematicians call a connection seems equivalent (or nearly so) to what physicists call a gauge field. So this line of research seems to be aimed at opening a way to treat both geometry and matter as gauge fields, in a single Plebanski-type action. Later on, if the program is successful, one might consider some background-independent, nonperturbative way of quantizing this combined gauge theory of geometry and matter. But that is not what this paper is about. A Spin Foam quantization of the Plebanski action was given for example by Perez in 2002: http://arxiv.org/abs/gr-qc/0203058 Spin foam quantization of SO(4) Plebanski's action Alejandro Perez (Submitted on 15 Mar 2002) Adv.Theor.Math.Phys. 5 (2002) 947-968 For people unfamiliar with the term, spin foam is a kind of LATTICE GAUGE THEORY, constructed without assuming a prior metric geometry. So if the classical program initiated by Alexander Marciano Smolin were successful, one way to follow up on it would presumably be to quantize it in the context of a lattice gauge theory. I expect all these issues will be clearer in a few days, after Stephon Alexander's Tuesday seminar talk.