Holographic entanglement entropy and generalized entanglement temperature

Ashis Saha; Sunandan Gangopadhyay; Jyoti Prasad Saha

doi:10.1103/PhysRevD.100.106008

paper

Holographic entanglement entropy and generalized entanglement temperature

arXiv:1906.03159 · doi:10.1103/PhysRevD.100.106008

Abstract

In this work we study the flow of holographic entanglement entropy in dimensions $d \geq 3$ in the gauge/gravity duality set up. We observe that a generalized entanglement temperature $T_{g}$ can be defined which gives the Hawking temperature $T_{H}$ in the infrared region and leads to a generalized thermodynamics like law $E = (\frac{d - 1}{d}) T_{g} S_{R E E}$ , which becomes an exact relation in the entire region of the subsystem size $l$ , including both the infrared ( $l \to \infty$ ) as well as the ultraviolet ( $l \to 0$ ) regions. Furthermore, in the IR limit, $T_{g}$ produces the Hawking temperature $T_{H}$ along with some correction terms which bears the signature of short distance correlations along the entangling surface. Moreover, for $d \geq 3$ , the IR limit of the renormalized holographic entanglement entropy gives the thermal entropy of the black hole as the leading term, however, does not have a logarithmic correction to the leading term unlike the BTZ black hole ( $d = 2$ ) case. The generalized entanglement temperature $T_{g}$ also firmly captures the quantum mechanical to thermal crossover in the dual field theory at a critical value $l_{c}$ of the subsystem size in the boundary which we graphically represent for $A d S_{3 + 1}$ and $A d S_{4 + 1}$ black holes. We observe that this critical value $l_{c}$ where the crossover takes place decreases with increase in the dimension of the spacetime.

16 pages Latex, 5 figures, to appear in Phys. Rev. D

Holographic entanglement entropy and generalized entanglement temperature

Abstract

References in corpus (5)

Cited by in corpus (11)