Quasinormal modes prefer supersymmetry?

One ambiguity in loop quantum gravity is the appearance of a free parameter which is called the Immirzi parameter. Recently Dreyer has argued that this parameter may be fixed by considering the quasinormal mode spectrum of black holes, while at the price of changing the gauge group to SO(3) rather than the original one SU(2). Physically such a replacement is not quite natural or desirable. In this paper we study the relationship between the black hole entropy and the quasinormal mode spectrum in the loop quantization of $N=1\mathrm{}$ supergravity. We find that a single value of the Immirzi parameter agrees with the semiclassical expectations as well. But in this case the lowest supersymmetric representation dominates, fitting well with the result based on statistical consideration. This suggests that, so long as fermions are included in the theory, supersymmetry may be favored for the consistency of the low energy limit of loop quantum gravity.