Holographic entanglement entropy of the near horizon 1/4 BPS F−Dp bound states

Abstract

It was shown in Dey and Roy [J. High Energy Phys. 06 (2012) 129] that the near-horizon limit of the $1/4$ Bogomol'nyi-Prasad-Sommerfield, threshold $\mathrm{F}\mathrm{\text{\ensuremath{-}}}\mathrm{D}p$ (for $0\ensuremath{\le}p\ensuremath{\le}5$, $p\ensuremath{\ne}4$) bound-state solutions of type-II string theories give rise to space-time metrics endowed with Lifshitz scaling along with hyperscaling violation. Here we compute the holographic entanglement entropy of this system for all $p\ensuremath{\ne}4$ (for $p=4$ the space-time has ${\mathrm{AdS}}_{2}$ structure). For $p=3$, 5, we get the expected area-law behavior of the entanglement entropy. For $p=0$, 1, the entanglement entropy has new area-law violations and exhibits behavior which is in between the linear and logarithmic behaviors. For $p=2$, we get a logarithmic violation of the area law. We also compute the entanglement entropy at finite temperature and show that as the temperature rises, the entanglement entropy makes a crossover to the thermal entropy of the system. We thus obtain the string-theoretic realization of the holographic entanglement entropy and its various aspects, which were noted earlier for a generic metric with hyperscaling violation.