# Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole

## TL;DR

This paper calculates the entanglement entropy of ABJM theory via its gravity dual, including quantum corrections, thereby testing the AdS/CFT correspondence beyond the classical approximation.

## Contribution

It provides an explicit computation of black hole entropy with logarithmic corrections in supergravity, matching entanglement entropy results of ABJM theory beyond leading order.

## Key findings

- Black hole entropy with logarithmic correction computed
- Entanglement entropy matches supergravity results
- Supports AdS/CFT correspondence at quantum level

## Abstract

In this paper we discuss the supersymmetric localization of the 4D $\mathcal{N}=2$ off-shell gauged supergravity in the background of the $\textrm{AdS}_4$ neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary $\textrm{S}^1 \times \mathbb{H}^2$. We compute the large-$N$ expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.