Monstrous entanglement

TL;DR

This paper analyzes the entanglement and Renyi entropies of the Monster CFT, connecting field theory calculations with holographic duals, and providing explicit formulas and comparisons with bulk computations.

Contribution

It provides explicit short interval expansion formulas for Renyi entropies in extremal CFTs, including the Monster CFT, and compares these with holographic bulk calculations.

Findings

Exact agreement of low-temperature corrections with universal predictions

Matching of boundary calculations with bulk one-loop partition functions

Insights into entanglement structure of extremal CFTs

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 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.