Abstract
We have obtained the equation of the extremal hypersurface by considering the Jacobson–Myers functional and computed the entanglement entropy. In this context, we show that the higher derivative corrected extremal surfaces cannot penetrate the horizon. Also, we have studied the entanglement temperature and entanglement entropy for low excited states for such higher derivative theories when the entangling region is of the strip type.
Highlights
The study of the entanglement entropy in the AdS/CFT context [1] has attracted a lot of attention due to its potential application in condensed matter systems as well as in quantum information theories
The question that we ask: Do we still expect to see a similar first law like relation even after the inclusion of the higher derivative term to the holographic entanglement entropy functional? If yes, how does the ‘entanglement temperature’ go with the length, ? And how does the proportionality constant behave as a function of d? We show that there exists a first law like relation even with the higher derivative term to the holographic entanglement entropy functional and the relation between the ‘entanglement temperature’ and the size is same as mentioned above
If we look at the expression of the holographic entanglement entropy, which is proportional to the area, eq(130) for AdS spacetime, it follows that
Summary
The study of the entanglement entropy in the AdS/CFT context [1] has attracted a lot of attention due to its potential application in condensed matter systems as well as in quantum information theories. We revisit such a computation but for a d dimensional CFT, i.e., for bulk AdS spacetime and the result to the linear order in the coupling λ1 can be summarized as follows: (a) The divergent term coming from UV goes in the same way as in the absence of the higher derivative term to the entanglement entropy functional, i.e., like 2−d, whereas (b) the finite term, the coefficient of r2−d, where r is the turning point, depends on the coupling λ1 very non-linearly but we determine the functional form only to linear order The answer to this question is that upon inclusion of the higher derivative term of the type as in eq(36) to the action of the embedding field make the spatial hypersurface not to penetrate the horizon It is suggested recently, by studying the low excited states [23], that the entanglement entropy obeys a law like that of the first law of thermodynamics, Tent∆S = ∆E. Some of the expression of the solution of the embedding field with the higher derivative term to the area functional has been relegated to Appendix B
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