What are the pros and cons of Causal Dynamical Triangulation (CDT)?

String theory and Loop Quantum Gravity are the two main approaches to Quantum Gravity so it's not perhaps suprising that we don't hear too much about other approaches particularly given the hype associated with the first approach.

Like LQG, dynamical triangulations is background independent. This simply means that they allow spacetime to be dynamical as it is in GR and unlike String Theory where it is fixed. It's also a non-perturbative approach unlike traditional techniques in QFT which are primarily perturbative.

It's based upon taking seriously the formal gravitational path integral which is essentially Feynmans path integral but using the Einstein-Hilbert action from GR and discretising spacetime.

Renate Loll points out in one talk that a 'compelling' feature of CDT is that spacetime dimension at the Planck scale approaches two rather than the four spacetime dimensions we know macroscopically.

A good overview is in this review paper by Ambjorn, Jurkiewicz and Loll.

CDT is in agreement with the RG approaches, and with LQG and other spin foam approaches in many things.

Both asymptotic safety (also becoming a major power in quantum gravity) and cdt states that there is an UV fixed point, around which the continuum theory can be restored. There the spacetime dimension reduces to 2 or 1.5. (at close distances)

I say or, because in a-safety 2 naturally poops out from the equations. In CDT it strongly depends on the point in the phase diagram. Currently there are 2 candidate points for the UVFP in CDT, at one it is d = 2, at the other it is 1.5. (both has its arguments)

The large scale dimensionality / hausdorff dimension is still 4 in most of these models (a-safe, cdt, lqg, causal sets).

As Astrid Eichorn said once in a seminar, quantum gravity is a huge elephant, and quantum gravity researchers are like blind people touching it from different sides. Someone touches the tail and thinks these are strings, one touches the skin and feels the coarse graining, one touches it from the front to feel the trunk (-ation ) , one hides under because its safe.. :)

we should work together, because apart from stringists the number of quantum gravitists is small.