QG has several approaches developing rapidly and it's not easy to maintain perspective. I'll update a rough outline map made earlier. We can use it to help know what papers to expect during the next couple of months and what developments to be prepared for. A. Three main sectors of Loop-community work: 1. Marseille new vertex suggested review = latest Rovelli et al (what I think will probably be QG paper of the year) 2. Penn State cosmology suggested review = Ashtekar's latest new feature = Bojowald on big bang nucleosynthesis 3. Perimeter dynamic topology both geometry and matter emerge from topology of fourvalent braid network states these states evolve by local moves which change how neighbor vertices are connected. No current review, but see recent papers by Smolin and Wan. Work in preparation by Bilson-Thompson, Hackett, Kauffman (look for "Sun-Jon-Louis" paper) B. Other approaches to watch (several have no minimal scale, in other words scale -> 0 ) 1. Legoblock path integral Loll's review just came out (CDT lets the size of the blocks go to zero) 2. Running couplings--going with the flow Percacci's review, "Asymptotic Safety" (Reuter-Percacci let the energy scale k go to infinity) 3. Hodge star gravity, where the Hodge dual replaces metric d.o.f. Krasnov's review just came out "Non-metric gravity: a status report" (see section 3 on Renormalizability) 4. Garrett Lisi's E8 gravity+matter----representing geometry + matter with an E8 connection C. Dark horses: 1. Pereira and Aldrovandi's deSitter GR---a bold idea that runs a severe risk of being falsified by TeV gammaray telescope data. A fairly complete P and A paper on deS GR just appeared. So we have an up-to-date account of the status of their theory. Now it's up to astronomers to confirm or refute. 2. Jesper Grimstrup LQG + NCG---another risky project: putting Connes standard particle model into LQG. Last paper was in 2006. Hopefully something from Aastrup and Grimstrup before long. ==================== Have review or status report papers for 2007 in these cases: A1. (Rovelli group et al) A2. (Ashtekar Bojowald et al) B1. (Loll group) B2. (Reuter Percacci et al) B3. (Krasnov) B4. (Lisi) C1. (Pereira Aldrovandi) Do not have 2007 review or status report in these cases: A3. (Smolin group) C2. (Grimstrup...) ================= A couple of things to think about: For one, how this is going to look around 1 July when there is the big international QG conference in UK called "QG2 2008"? The main organizer John Garrett will almost certainly have a different map in mind. Some of the people in my outline here will give invited plenary talks at QG^2. Which ones, and specifically about what? For another, which of these approaches can merge constructively, or be shown to be equivalent? For example, Smolin dynamic topology approach uses FOURvalent vertices to describe a braided webwork from which geometry and matter should emerge. In a fourvalent web one can replace every vertex by a tetrahedron, and have something looking like a LOLL setup. So at least a superficial resemblance, but nothing said here comparing the dynamics of moves by which the webwork and the triangulation evolve. Pachner moves come up in both cases, but don't jump to conclusions At this point the two approaches look quite different. For example Pereira and Aldrovandi approach has a term called the conformal current related to how rapidly space is expanding. In several versions of LQG one needs to control the amplitude with which new vertices are created. If P&A should turn out to be compatible with spinnetwork dynamics, does their conformal current give a handle on that applitude? P&A seem to have a mathematically nice way of doing what used to be called deformed special relativity (DSR). They don't mess with deforming special, they go right to general and use deSitter in place of Lorentz/Poincaré. The results are a little hair-raising at first sight but very interesting. It might actually be highly suitable as a classical limit for some version that Smolin Rovelli et al are working on. So convergence is another thing to think about in the context of this map.