When is entanglement entropy the same as free energy?

I am given the feeling that there exists scenarios when this equality holds. Can anyone state/refer to the situations?

One case that I hear of is that for $2+1$ CFTs the entanglement entropy across a spatial disk is the same as the free energy of the CFT system on a $S^2 \times S^1$ (or $S^3$?)

• What is the exact correct statement?

• I am told that this paper http://arxiv.org/pdf/1102.0440v2.pdf "proves" the above but despite reading this paper a few times I can't locate this argument! (...may be I am missing something very badly!...)

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1 Answer

The proof is in the section 4.2 of the paper, with the claim being made in the last paragraph of that section. See also

http://arxiv.org/abs/1012.1548

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Motl Thanks for your efforts! So you mean that 4.2 of my linked 1102.0440 proves this free energy equality? – user6818 Aug 17 '13 at 23:40
Yes, wouldn't it be easier for both of us to look at the section than to ask again whether you should look? – Luboš Motl Aug 18 '13 at 5:58