Ashoke Sen has written a paper http://arxiv.org/abs/1205.0971 which uses path integrals in Euclidean gravity to compute "Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions". Sen starts by listing several varieties of extremal black hole for which a string theory calculation of such corrections agrees with a Euclidean-gravity calculation of the corrections. He notes that there is no such stringy calculation for non-extremal black holes (such as the ones of astrophysical interest), but loop quantum gravity does make claims in this area, some of which have been discussed on this site (e.g. Bianchi 2010, Engle Noui Perez 2009). Sen performs the Euclidean gravity calculation and finds that it disagrees with the LQG values. Lubos Motl writes that this is the end for LQG. Well, we'll see. While I would like to see a discussion about how LQG could reproduce this result (or why it can be ignored), I also find it interesting that Euclidean gravity does agree with string theory here, several times over. Why exactly is that? Can you "see" the stringiness already in the Euclidean gravity, if you know what to look for? A minor twist is that Sen's calculations are for Schwarzschild black holes in pure d=4 gravity, a theory which I believe is in string theory's "swampland" - the set of theories which can't be obtained as a low-energy limit of string theory (the name is meant to suggest the opposite of the "landscape" of field theories which can be so obtained). So it shouldn't actually be possible to reproduce Sen's exact calculation within string theory either. But this is a minor detail because the method of calculation should easily be adjusted to include the effects of the other standard-model fields, and if string theory does contain the standard model, then this adjusted result is definitely one it should be able to produce. The primordial paper in which the prototype of Sen's calculation first appears is apparently http://arxiv.org/abs/hep-th/9407001 You may see, for example, the origin of the denominator "45" in Sen's formula, in equation 87 of this paper from 1994. So if you're trying to use these Euclidean results as a guide to LQG theory construction, this is the part that you want to reverse-engineer. Perhaps this paper could be fruitfully contrasted with "Bianchi 2010", linked above. And I'll also throw in 't Hooft's "The holographic mapping of the Standard Model onto the black hole horizon, Part I: Abelian vector field, scalar field and BEH Mechanism", which is not directly about the entropy, but which is aiming at the description of a black hole within the standard model. edit #1: A bridge to 't Hooft's paper might be found in http://arxiv.org/abs/1104.3712 by Sergey Solodukhin, author of the 1994 calculation, when he discusses 't Hooft's 1985 "brick wall model", which is an important part of history both for the holographic principle and for black hole entropy calculations. edit #2: Perhaps I should spell out that, although this is naturally another LQG vs string topic, the core calculation here does not originate in either framework, it comes from Euclidean gravity. Sen has calculated these corrections to the Bekenstein-Hawking entropy for a Schwarzschild black hole in d=4 pure gravity, and it should be easy to adjust his procedure to compute the corrections if there are other fields as well. The question for both LQG and string is then 1) what attitude to take towards these calculations, agree or disagree, and if agree, 2) explain how to produce them within the LQG or string framework. There is also the tangential (but very interesting) question of how these calculations relate to 't Hooft 1985 (the brick wall model) and 't Hooft 2005 (holography for a standard model black hole).