We will discuss the canonical partition function for quantum black holes in the approach of
Loop Quantum Gravity (LQG). We argue that any quantum theory of gravity in which the hori-
zon area is built of non-interacting constituents cannot yield qualitative corrections to the
Bekenstein-Hawking (B-H) area law, but corrections to the area law can arise as a conse-
quence additional constraints inducing interactions between the constituents. In LQG this
is implemented by requiring spherical horizons. We will see that canonical approach for LQG
favours a logarithmic correction to the B-H law with a coefficient of −1/ 2 , (just like in the case of
counting entropy), contrary to the coefficient being +1/2, discussed recently in the literature.
The initial calculation of the partition function uses certain approximations that
do not qualitatively affect the expression for the black hole entropy. We will also
discuss the quantitative corrections to these results when the simplifying approximations
are relaxed and the full LQG spectrum is dealt with. We will see how these corrections can be
recovered to all orders in perturbation theory.
