Editing Loop quantum gravity (section)

== Gravitons, string theory, supersymmetry, extra dimensions in LQG ==
{{main| Graviton| string theory| supersymmetry| Kaluza–Klein theory| supergravity}}
Some quantum theories of gravity posit a spin-2 quantum field that is quantized, giving rise to gravitons. In string theory, one generally starts with quantized excitations on top of a classically fixed background. This theory is thus described as background dependent. Particles like photons as well as changes in the spacetime geometry (gravitons) are both described as excitations on the string worldsheet. The background dependence of string theory can have physical consequences, such as determining the number of quark generations. In contrast, loop quantum gravity, like general relativity, is manifestly background independent, eliminating the background required in string theory. Loop quantum gravity, like string theory, also aims to overcome the nonrenormalizable divergences of quantum field theories.

LQG does not introduce a background and excitations living on such a background, so LQG does not use gravitons as building blocks. Instead one expects that one may recover a kind of semiclassical limit or weak field limit where something like "gravitons" will show up again. In contrast, gravitons play a key role in string theory where they are among the first (massless) level of excitations of a superstring.

LQG differs from string theory in that it is formulated in 3 and 4 dimensions and without supersymmetry or [[Kaluza–Klein theory|Kaluza–Klein]] extra dimensions, while the latter requires both to be true. There is no experimental evidence to date that confirms string theory's predictions of supersymmetry and Kaluza–Klein extra dimensions. In a 2003 paper "A Dialog on Quantum Gravity",{{sfn|Rovelli|2003|pp=1509–1528}} Carlo Rovelli regards the fact LQG is formulated in 4 dimensions and without supersymmetry as a strength of the theory as it represents the most [[parsimonious]] explanation, consistent with current experimental results, over its rival string/M-theory. Proponents of string theory will often point to the fact that, among other things, it demonstrably reproduces the established theories of general relativity and quantum field theory in the appropriate limits, which loop quantum gravity has struggled to do. In that sense string theory's connection to established physics may be considered more reliable and less speculative, at the mathematical level. Loop quantum gravity has nothing to say about the matter (fermions) in the universe.

Since LQG has been formulated in 4 dimensions (with and without supersymmetry), and M-theory requires supersymmetry and 11 dimensions, a direct comparison between the two has not been possible. It is possible to extend mainstream LQG formalism to higher-dimensional supergravity, general relativity with supersymmetry and Kaluza–Klein extra dimensions should experimental evidence establish their existence. It would therefore be desirable to have higher-dimensional Supergravity loop quantizations at one's disposal in order to compare these approaches. A series of papers have been published attempting this.{{sfn|Bodendorfer|Thiemann|Thurn|2013a|p=045001}}{{sfn|Bodendorfer|Thiemann|Thurn|2013b|p=045002}}{{sfn|Bodendorfer|Thiemann|Thurn|2013c|p=045003}}{{sfn|Bodendorfer|Thiemann|Thurn|2013d|p=045004}}{{sfn|Bodendorfer|Thiemann|Thurn|2013e|p=045005}}{{sfn|Bodendorfer|Thiemann|Thurn|2012|p=205}}{{sfn|Bodendorfer|Thiemann|Thurn|2013f|p=045006}}{{sfn|Bodendorfer|Thiemann|Thurn|2013g|p=045007}} Most recently, Thiemann (and alumni) have made progress toward calculating black hole entropy for supergravity in higher dimensions. It will be useful to compare these results to the corresponding super string calculations.{{sfn|Bodendorfer|Thiemann|Thurn|2014|p=055002}}{{sfn|Bodendorfer|2013|pp=887–891}}