Why are string theorists interested in entanglement entropy?

Question

I have been reading some papers on Ryu-Takyanagi but I am not seeing a good explanation as to why entanglement entropy of the boundary CFT a good observable to probe the possible bulk quantum gravity.

Is there any sense of non-renormalizability about this observable?
Any kind of deformation invariance? (like Witten index)
Is it even defined for CFTs at finite temperature or at arbitrary coupling?

Comments

Possibly related: Entanglement entropy from a holographic viewpoint (PDF)

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Could this Maldacena talk be helpful? 

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Yes, I remember that Lumo has mentioned entanglement entropy in one of his ER/EPR TRF posts too. Might be related to the strenght or the ER bridge?

Answer 1

Partial answer (only to the first part of your question):

I read through this paper (PDF), and I don't see anything exceptionally surprising about the entanglement entropy being a suitable observable to probe the dual quantum gravity theory. The entanglement entropy \(S\) is equal to \(\frac{A}{4G_N}\), which is of course related to the possible bulk quantum gravity. You can read more on pg 2 of the linked paper (pg 2 of the paper, not of the PDF file).