Monstrous entanglement

Abstract 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 Rényi entropies of this theory along with other extremal CFTs. The Rényi entropies of a single interval on the torus are evaluated using the short interval expansion. Each order in the expansion contains closed form expressions in the modular parameter. The leading terms in the q-series are shown to precisely agree with the universal corrections to Rényi entropies at low temperatures. Furthermore, these results are shown to match with bulk computations of Rényi entropy using the one-loop partition function on handlebodies. We also explore some features of Rényi entropies of two intervals on the plane