Extremal black hole

Routing protocol

Entropy (arrow of time)

Legendre transformation

Supersymmetry

Physics

Boltzmann equation

Partition function (quantum field theory)

Computer network

Boltzmann's entropy formula

Mathematical physics

Computer science

Black hole (networking)

Quantum mechanics

Black hole thermodynamics

Routing (electronic design automation)

Link-state routing protocol

Thermodynamics

Journal of High Energy Physics

ABSTRACT We present a holographic derivation of the entropy of supersymmetric asymp­totically AdS 5 black holes. We define a BPS limit of black hole thermodynamics by first focussing on a supersymmetric family of complexified solutions and then reaching extremality. We show that in this limit the black hole entropy is the Legendre transform of the on-shell gravitational action with respect to three chemical potentials subject toa con­straint. This constraint follows from supersymmetry and regularity in the Euclidean bulk geometry. Further, we calculate, using localization, the exact partition function of the dual $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 SCFT on a twisted S 1 × S 3 with complexified chemical potentials obeying this constraint. This defines a generalization of the supersymmetric Casimir energy, whose Legendre transform at large N exactly reproduces the Bekenstein-Hawking entropy of the black hole.

Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes