TY - JOUR

T1 - Refined holographic entanglement entropy for the ads solitons and ads black holes

AU - Ishihara, Masafumi

AU - Lin, Feng Li

AU - Ning, Bo

N1 - Funding Information:
F.-L.L. thanks Xie Chen, Ching-Yu Huang, Wei Li, Hong Liu and Frank Pollmann for discussions, especially thanks Tadashi Takayanagi for classifying some subtle issues relevant to our revision. We thank Pei-Hua Liu for drawing the MERA figures. F.-L.L. is supported by Taiwanʼs NSC grants (grant Nos. 100-2811-M-003-011 and 100-2918-I-003-008 ). We thank the support of NCTS .

PY - 2013/7/21

Y1 - 2013/7/21

N2 - We consider the refinement of the holographic entanglement entropy for the holographic dual theories to the AdS solitons and AdS black holes, including the corrected ones by the Gauss-Bonnet term. The refinement is obtained by extracting the UV-independent piece of the holographic entanglement entropy, the so-called renormalized entanglement entropy which is independent of the choices of UV cutoff. Our main results are: (i) the renormalized entanglement entropies of the AdSd+1 soliton for d=4, 5 are neither monotonically decreasing along the RG flow nor positive-definite, especially around the deconfinement/confinement phase transition; (ii) there is no topological entanglement entropy for AdS5 soliton even with Gauss-Bonnet correction; (iii) for the AdS black holes, the renormalized entanglement entropy obeys an expected volume law at IR regime, and the transition between UV and IR regimes is a smooth crossover even with Gauss-Bonnet correction; (iv) based on AdS/MERA conjecture, we postulate that the IR fixed-point state for the non-extremal AdS soliton is a trivial product state.

AB - We consider the refinement of the holographic entanglement entropy for the holographic dual theories to the AdS solitons and AdS black holes, including the corrected ones by the Gauss-Bonnet term. The refinement is obtained by extracting the UV-independent piece of the holographic entanglement entropy, the so-called renormalized entanglement entropy which is independent of the choices of UV cutoff. Our main results are: (i) the renormalized entanglement entropies of the AdSd+1 soliton for d=4, 5 are neither monotonically decreasing along the RG flow nor positive-definite, especially around the deconfinement/confinement phase transition; (ii) there is no topological entanglement entropy for AdS5 soliton even with Gauss-Bonnet correction; (iii) for the AdS black holes, the renormalized entanglement entropy obeys an expected volume law at IR regime, and the transition between UV and IR regimes is a smooth crossover even with Gauss-Bonnet correction; (iv) based on AdS/MERA conjecture, we postulate that the IR fixed-point state for the non-extremal AdS soliton is a trivial product state.

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U2 - 10.1016/j.nuclphysb.2013.04.003

DO - 10.1016/j.nuclphysb.2013.04.003

M3 - Article

AN - SCOPUS:84876742991

VL - 872

SP - 392

EP - 426

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -