Lee Smolin, Penn State
Much of the most interesting recent progress in quantum gravity concerns approaches that are fundamentally discrete, in the sense that it is assumed from the beginning that space or spacetime is built up out of discrete structures. This summer about 40 physicists working on a variety of such approaches met for two weeks at Saint John's College in Santa Fe to discuss recent progress in these areas. Among the directions that were represented were dynamical triangulations, random surface theory, Regge calculus, causal sets, decoherent histories, topological quantum field theory and lattice and path integral approaches to non-perturbative quantum gravity.
The workshop was sponsored by Los Alamos National Laboratory and organized by Emil Mottola. The structure was informal and allowed much time for discussions that probed the key issues in these areas. Here is a summary of some of the highlights of the meeting. (for more details as well as names and references I refer the interested reader to the conference web site, http://nqcd.lanl.gov/people/emil/sgrav.html.
-Two dimensional random surface theory seems by now to be very well understood. The situation with four dimensional dynamical triangulations is better, and the physics of the different phases is better understood. But the order of the phase transition is still debated, although most participants seemed convinced by recent numerical evidence favoring a weakly first order transition. This led to lively discussion as the standard scenario would imply that only theories with a first order transition may have a continuum limit. However, there were proposals that theories with first order transitions may still have critical behavior. Another possibility discussed was that a second order critical point might be found by varying a parameter associated with the measure of the theory.
-There was lively discussion about the longstanding issue of the relationship between Regge calculus and dynamical triangulations. Unfortunately, most of the main proponents of the Regge calculus approach were absent, so a real resolution was not possible. However, it is clear there has been progress on the issue of the measure of the path integral in Regge calculus.
-There are new and apparently very useful techniques for applying the renormalization group to dynamical triangulations.
-There has recently been a lot of progress in the causal set program. One new idea is that directed percolation models may give examples of causal sets which naturally have low spatial dimension. These make possible a new interchange with statistical physics in which methods from the study of directed percolation and cellular autonota may be applied to elucidate non-perturbative behavior in quantum gravity.
-There are new connections between canonical quantum gravity, causal sets, triangulations and topological quantum field theory.
-Analytical techniques may be applied to quantum gravity to uncover the physics of the infrared behavior. Under certain assumptions this leads to surprising predictions about gravitation at cosmological distance scales. These and other analytical calculations may be compared with the results of numerical simulations, leading to a very healthy interaction of computational and analytical methods.