  The Monster CFT plays an important role in moonshine and is also conjectured
to be the holographic dual to pure gravity in AdS3. We investigate the
entanglement and Renyi entropies of this theory along with other extremal CFTs.
The Renyi entropies of a single interval on the torus are evaluated using the
short interval expansion. Each order in the expansion contains closed form
expressions of the modular parameter. The leading terms in the q-series are
shown to precisely agree with the universal corrections to Renyi entropies at
low temperatures. Furthermore, these results are shown to match with bulk
computations of Renyi entropy using the one-loop partition function on
handlebodies. We also explore some features of Renyi entropies of two intervals
on the plane.
