Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole
Jun Nian, Xinyu Zhang
TL;DR
This work uses supersymmetric localization of 4D $\mathcal{N}=2$ off-shell gauged supergravity on the AdS$_4$ neutral topological black hole to compute the large-$N$ gravity partition function and extract the black hole entropy with a logarithmic correction. The authors demonstrate that the bulk entropy matches the ABJM theory's entanglement entropy across a circle in the boundary, up to stringy corrections, thereby testing AdS/CFT beyond the leading classical term. They derive the gravity-side partition function via a TBH background, perform holographic renormalization, and apply steepest-descent to obtain the asymptotics, revealing a leading $-\frac{\sqrt{2}\pi}{3} k^{1/2} N^{3/2}$ term and a $-\frac{1}{4}\log N$ correction, in agreement with the dual field theory up to subleading effects. The results reinforce the TBH/$q$SCFT framework as a precise setting for comparing boundary entanglement entropy and bulk black hole entropy, while also pointing to stringy effects that encode subleading discrepancies.
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.