Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole

Abstract

In this paper we discuss the supersymmetric localization of the 4D $\mathcal{N}=2$ off-shell gauged supergravity in the background of the ${\text{AdS}}_4$ neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary ${\text{S}}^1\times {\mathbb{H}}^2$. 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.

34 pages, 1 figure; minor changes in v2; references added in v3, published version in JHEP

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Cited by in corpus (15)

• Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
• Black hole entropy in massive Type IIA
• Topologically twisted indices in five dimensions and holography
• Microscopic Entropy of Rotating Electrically Charged AdS${}_4$ Black Holes from Field Theory Localization
• Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• 6D attractors and black hole microstates
• On the quantum entropy function in 4d gauged supergravity
• Black hole microstate counting in Type IIB from 5d SCFTs
• Supersymmetric Rényi entropy and charged hyperbolic black holes
• Gravitational Cardy Limit and AdS Black Hole Entropy
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS${}_5$
• Universal Entropy and Hawking Radiation of Near-Extremal AdS${}_4$ Black Holes
• Quantum entropy of BMPV black holes and the topological M-theory conjecture