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arXiv 1406.5593hep-th
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纠缠熵中的弱极小区域

Weak Minimal Area In Entanglement Entropy

Shesansu Sekhar Pal, Shubhalaxmi Rath

摘要:

在全息计算纠缠熵中,我们重新考虑了Ryu-Takayanagi的最小面积条件。特别是Legendre检验和Jacobi检验。弱极小性的必要条件通过Legendre检验,其充分性通过Jacobi检验。对于具有带状纠缠区的AdS黑洞,我们证明了正是这种极小性条件使超曲面不穿过视界,这与{ \it Engelhardt et al.}和{ \it Hubeny}使用不同的方法。此外,对纠缠熵泛函中高阶导数项的弱极小条件的要求对Gauss-Bonnet耦合提出了一个约束:即耦合值$λ_a< \f{(d-3)}{4(d-1)}$必须有一个上界.

英文摘要:

We re-visit the minimal area condition of Ryu-Takayanagi in the holographic calculation of the entanglement entropy. In particular, the Legendre test and the Jacobi test. The necessary condition for the weak minimality is checked via Legendre test and its sufficient nature via Jacobi test. We show for AdS black hole with a strip type entangling region that it is this minimality condition that makes the hypersurface not to cross the horizon, which is in agreement with that studied earlier by {\it Engelhardt et al.} and {\it Hubeny} using a different approach. Moreover, demanding the weak minimality condition on the entanglement entropy functional with the higher derivative term puts a constraint on the Gauss-Bonnet coupling: that is there should be an upper bound on the value of the coupling, $λ_a< \f{(d-3)}{4(d-1)}$.

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