Diverging black hole entropy from quantum infrared non-localities

Local higher-derivative corrections to the Einstein-Hilbert action yield sub-leading corrections to the Bekenstein-Hawking area law. Here we show that if the quantum effective action comprises a certain class of infrared non-localities, the entropy of large black holes generally diverges to either positive or negative infinity. In such theories, large spherically symmetric black holes would be either highly chaotic or thermodynamically impossible, respectively. In turn, this puts strong constraints on the Laurent expansion of the form factors in the effective action.