Yesterday there were some sessions on Lattice techniques aimed at non-specialists attending the ICHEP conference. Apparently the attendance was disappointing. That is not very surprising given the competition from other parallel sessions where new physics could be announced. Lattice theory has been around for a long time and mostly looks at QCD which is far from new.

As an ex-lattice gauge theorist myself I think there are some aspects of it that people working on more sexy subjects such as quantum gravity would benefit from understanding better. In particular they should understand how the phase diagram of QCD at high temperature and density is being charted using these non-perturbative methods. The reason they need to know this is that a similar phase structure should exist in quantum gravity and there is likely to be a strong (but approximate) correspondence through AdS/CFT duality that relates quantum gravity to a QCD-like theory.

In the QCD theory of the strong interactions there is believed to be a temperature known as the Hadgdorn temperature above which nuclear matter breaks down into a quark gluon plasma. This happens at around 10 billion degrees Kelvin. In quantum gravity according to string theory (if you don’t like string theory dont switch off, this is just a short diversion) there is another Hagdorn temperature at around the Planck scale. That’s about 10^{32} degrees Kelvin. What happens there?

According to string theory the length of strings becomes very large and effectively the concept of the string breaks down. Sometimes string theorists call this the topological phase of string theory because they think that spacetime loses its geometry in the hotter phase. The truth is that not much is known about what really happens because most of string theory is based on perturbative calculations and phase transitions are very non-perturbative. What might happen is that not only geometry of space-time is lost but topology too. In that case it should be called the non-topological phase, or pregeometric phase. To put it another way, spacetime evaporates. Even if you don’t believe in string theory you might still consider this possibility. Some non-string theorists talk about geometrogenesis which is the process of cooling from the high temperature pregeometric phase to the more familiar geometric phase at the start of the big bang.

For now we can get some feel for the phase structure of quantum gravity by looking at the phase structure of QCD which brings me to one of the ICHEP talks from yesterday. However I’ll do that in a separate post in case people get confused and think it was about quantum gravity.