  One ambiguity in loop quantum gravity is the appearance of a free parameter
which is called 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 quasi normal mode spectrum in the loop quantization of N=1
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, supersymemtry may be favored for the consistency of the low
energy limit of loop quantum gravity.
