I have read at different places that in 3 spacetime dimensions, there are NO propagating gravitational degrees of freedom. This seems to imply that we have only "non-propagating" degrees of freedom. What does that mean?
For concreteness, let me give two examples where I encountered this such statements:
In Supergravity by Freedman and Proeyen, authors say in Exercise 5.1: "This is the supersymmetric counterpart of the situation in gravity in $D=3$, where the field equation $R_{\mu\nu}=0$ implies that the full curvature tensor $R_{\mu\nu\rho\sigma}=0$. Hence no degrees of freedom."
On Quora, Shouvik Datta says: "the graviton in (2+1)-dimensions doesn't have any propagating degrees of freedom."
My best guess is that the fields involved in such cases do have some local degrees of freedom. But they don't interact with neighboring degrees of freedom. That's why any perturbation in the field at some point doesn't get propagated to anywhere else. But I might be utterly wrong.
If someone could contrast these non-propagating degrees against the propagating ones ( perhaps with the help of an analogy ), that would be great. Any references are also welcome.
