Graduate Are there any theorems restricting possible QG candidates?

[Kontilera]

String theory, being such a theoretically successful theory as it is but with no experiment to single it out as THE model among alternatives, Im left to wonder, which models can be excluded? Are there essential no-go theorems regarding the physics of a theory for QG?
Im aware of the Coleman-Mandula theorem, but are there also restrictions to, say, which geometrical objects that, when quantized, could give rise to fruitful models of our universe?

Thanks.

// Curious

 

[kodama]

arXiv:gr-qc/0306083 (gr-qc)
[Submitted on 18 Jun 2003 (v1), last revised 19 Jun 2003 (this version, v2)]
A Note On The Chern-Simons And Kodama Wavefunctions
Edward Witten