Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2012-03-28
Physics
High Energy Physics
High Energy Physics - Theory
51 pages, 26 figure;v2 few typos corrected
Scientific paper
We consider the refinement of the holographic entanglement entropy on a disk region for the holographic dual theories to the AdS solitons and AdS black holes, including the corrected ones by the Gauss-Bonnet term. The AdS soliton is dual to a gapped system with an IR fixed-point. The refinement is obtained by extracting the UV-independent piece of the holographic entanglement entropy. We then study the renormalization group (RG) flow of the refinement by tuning the linear size of the chosen disk region. Our main results are (i) the RG flow of the refinement decreases monotonically for most of the cases; (ii) there is no topological entanglement entropy for AdS$_5$ soliton even with Gauss-Bonnet correction; (iii) for the AdS black holes, the refinement obeys the volume law at IR regime, and the transition between UV and IR regimes is a smooth crossover; however, the crossover will turn into phase transition by the Gauss-Bonnet correction; (iv) for the AdS solitons, there are discontinuous phase transitions between the refinements at the UV and IR regimes which both obey the area law, and in some cases there is no saddle point near the phase transition; (v) based on AdS/MERA conjecture, we postulate that the IR fixed-point state for the non-extremal AdS soliton is a trivial product state.
Ishihara Masafumi
Lin Feng-Li
Ning Bo
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