Can we derive the Wheeler–DeWitt equations from string theory? Since they are both quantum gravity theory.
A simple way seems to be the following logic:
The Wheeler–DeWitt equation is the canonically quantised version of the energy and momentum constraints in classical general relativiy, and that's equivalent to the Einstein field equation. In string theory we can also derive the Einstein field equation as the renormalization group flow of the metric as a coupling constant. But I 'm not sure if it is the right way and I didn't see any discussion about this...
