Unfortunately, so far... a truly background independent formulation of string theory has not been achieved... [It is] often called the search for M t… - Lee Smolin

The suggestion was that a positive energy proof for general relativity could be gotten by restricting supergravity to its bosonic sector, which is general relativity.

Calculation establishes that a quantum positive energy theorem may be possible using a representation based on the Ashtekar connection. Left open is a key question of whether this use of the Ashtekar connection is necessary or whether a positive quantum energy result can be achieved for representations based on other connections, i.e., for [other] values of the Immirzi parameter.

In string theory one studies strings moving in a fixed classical spacetime. ...what we call a background-dependent approach. ...One of the fundamental discoveries of Einstein is that there is no fixed background. The very geometry of space and time is a dynamical system that evolves in time. The experimental observations that energy leaks from binary pulsars in the form of gravitational waves—at the rate predicted by general relativity to the... accuracy of eleven decimal places—tell us that there is no more a fixed background of spacetime geometry than there are fixed crystal spheres holding the planets up.