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On the On-Shell: The Action of AdS$_4$ Black Holes
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abstract
We compute the on-shell action of static, BPS black holes in AdS$_4$ from ${\cal N}=2$ gauged supergravity coupled to vector multiplets and show that it is equal to minus the entropy of the black hole. Holographic renormalization is used to demonstrate that with appropriate boundary conditions on the scalar fields, the divergent and finite contributions from the asymptotic boundary vanish. The entropy arises from the extrinsic curvature on $\Sigma_g\times S^1$ evaluated at the horizon, where $\Sigma_g$ may have any genus $g\geq 0$. This provides a clarification of the equivalence between the partition function of the twisted ABJM theory on $\Sigma_g\times S^1$ and the entropy of the dual black hole solutions. It also demonstrates that the complete entropy resides on the AdS$_2\times \Sigma_g$ horizon geometry, implying the absence of hair for these gravity solutions.
Forward citations
Cited by 3 Pith papers
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Equivariant localization for $D=4$ gauged supergravity
Supersymmetric Euclidean D=4 N=2 gauged supergravity actions and fluxes localize onto R-symmetry fixed points, proving large-N SCFT free-energy formulas and UV-IR relations.
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Aspects of AdS$_2$ classification in M-theory: Solutions with mesonic and baryonic charges
The paper gives necessary and sufficient geometric conditions for N=(1,0) AdS2 solutions in M-theory with SU(4)-structure, and presents numerical evidence for a new Q^{1,1,1} solution with both mesonic and baryonic charges.
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The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS$_4$ Black Hole Entropy
The leading term of the ABJM topologically twisted index in the 't Hooft limit equals the Bekenstein-Hawking entropy of the dual AdS4 black holes, with sub-leading terms including a predicted -(7/6) log lambda contribution.
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