Though string theorists like to point out that theirs is the most developed theory to unite general relativity and quantum physics (at times they even seem clueless that alternatives exist), sometimes it seems like nearly every physicist has come up with some plan to combine the two — they just don’t have the support that string theorists have.
Most of these alternate theories start with the same idea as loop quantum gravity — that space is made up of small, discrete units that somehow work together to provide the space-time that we all know and love (relatively speaking, that is). Despite the fact that scientists don’t know much about these units of space, some theorists can analyze how they might behave and use that information to generate useful models.
Here are some examples of these other quantum gravity approaches:
Causal dynamical triangulations (CDT): CDT models space-time as being made up of tiny building blocks, called 4-simplices, which are identical and can reconfigure themselves into different curvature configurations.
Quantum Einstein gravity (or “asymptotic safety”): Quantum Einstein gravity assumes that there’s a point where “zooming in” on space-time stops increasing the force of gravity.
Quantum graphity: In the quantum graphity model, gravity didn’t exist in the earliest moments of the universe because space itself doesn’t exist on the small length and high energy scales involved in the early universe.
Internal relativity: This model predicts that you can start with a random distribution of quantum spins and get the laws of general relativity to come out of it.
Of course, any of these approaches could advance either string theory or loop quantum gravity, instead of leading off in a new direction. Some of the principles may prove fruitful, but only when applied in the framework of one of the other theories. Only time will tell what insights, if any, come out of them and if they can be applied to give meaningful results.