We point out that the entropy of (near) extremal black holes can be interpreted as the entanglement entropy of dual conformal quantum mechanics via ${\mathrm{AdS}}_2/{\mathrm{CFT}}_1$. As an explicit example, we study near extremal Banados-Teitelboim-Zanelli black holes and derive this claim from ${\mathrm{AdS}}_3/{\mathrm{CFT}}_2$. We also analytically compute the entanglement entropy in the two dimensional CFT of a free Dirac fermion compactified on a circle at finite temperature. From this result, we clarify the relation between the thermal entropy and entanglement entropy, which is essential for the entanglement interpretation of black hole entropy.

• Received 4 January 2008

DOI:https://doi.org/10.1103/PhysRevD.77.064005