  The quantum correction to the entanglement entropy of the event horizon is
plagued by the UV divergence due to the infinitely blue-shifted near horizon
modes. The resolution of this UV divergence provides an excellent window to a
better understanding and control of the quantum gravity effects. We claim that
the key to resolve this UV puzzle is the transplanckian dispersion relation. We
calculate the entanglement entropy using a very general type of transplanckian
dispersion relation such that high energy modes above a certain scale are
cutoff, and show that the entropy is rendered UV finite. We argue that modified
dispersion relation is a generic feature of string theory, and this boundedness
nature of the dispersion relation is a general consequence of the existence of
a minimal distance in string theory.
