Monstrous entanglement

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.