What is the significance of 2D quantum gravity in theoretical physics?

[maddy]

What exactly is 2D quantum gravity? Is it just a simplification of 3D quantum gravity i.e. to get results easier?

 

[marcus]

What exactly is 2D quantum gravity? Is it just a simplification of 3D quantum gravity i.e. to get results easier?

hi maddy, people do various styles of quantum gravity so let's say for example that we are talking about the recent venture into
dynamical triangulations 2D quantum gravity made by Smolin and Markopoulou
hep-th/0409057

there 2D means 1+1, namely 1 spatial dimension and 1 time dimension

earlier this year there was a dynamical triangulations 4D quantum gravity paper by Ambjorn et all. In that case 4D meant 3+1, namely 3 spatial and one time dimension.
hep-th/0404156
"Emergence of a 4D world from causal quantum gravity"

People also do 3D quantum gravity meaning 2+1.

Loop Quantum Gravity can be done in any dimension but the most usual is 3+1.

It does make the formulas simpler to work in a reduced dimension, sometimes people call it a "toy model"
In the case of the Markopoulou/Smolin paper they had an idea they want to apply to 4D but are making an initial trial of it in the 2D case where it is simpler to calculate and see what is going on

 

[selfAdjoint]

One of the important features of 2d (i.e. 1+1D) general relativity is that the field in 2D has no local degrees of freedom. What this goobeldygook means is that every solution of the equations covers the whole 2D spacetime, not just a piece of it. This simplifies a lot, just as it obscures a lot. Like many another toy model it is tremendously useful, but you can't push the conclusions you get from it too far.

Just because of that no local degrees of freedom stuff, many trial theories work fine in 2D but are like pulling teeth to extend to 3 and 4D. This is true of classical variations on GR as well as various QG efforts.

 

[arivero]

For a hint, calculate the dimensions of Newton constant for 1+1 and 2+1 gravity.