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arXiv 2103.06893hep-thcond-mat.stat-mechquant-ph
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全息BCFTs中的世界尽头膜谱

Spectrum of End of the World Branes in Holographic BCFTs

Masamichi Miyaji, Tadashi Takayanagi, Tomonori Ugajin

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22 pages, 4 figures
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摘要：

研究了共形场论中两个正则边界态的重叠问题。正则边界态通过AdS/BCFT与AdS黑洞中的世界尽头膜对偶。因此，它们可以被看作是单面黑洞的微观态。由于开闭对偶性，两个不同正则化边界状态之间的这种重叠被指数抑制为$\langle ψ_{a} | ψ_{b} \rangle \sim e^{-O(h^{(min)}_{ab})}$，其中$h^{(min)}_{ab}$是连接两个不同边界$a$和$b$的开弦的最低能量。我们的重力对偶分析导致纯AdS $_3$重力的$h^{(min)}_{ab} = c/24$。这表明全息边界态是所有左右对称态中的随机矢量，其数量由所有黑洞微观态数量的平方根给出。我们还在高维中进行了类似的计算，发现$h^{( min)}_{ab}$依赖于膜的张力。在我们的全息边界态分析中，与以前计算二维引力中微观态的内积不同，我们可以直接从壳层上的引力作用计算出内积的非对角元素。

英文摘要：

We study overlaps between two regularized boundary states in conformal field theories. Regularized boundary states are dual to end of the world branes in an AdS black hole via the AdS/BCFT. Thus they can be regarded as microstates of a single sided black hole. Owing to the open-closed duality, such an overlap between two different regularized boundary states is exponentially suppressed as $\langle ψ_{a} | ψ_{b} \rangle \sim e^{-O(h^{(min)}_{ab})}$, where $h^{(min)}_{ab}$ is the lowest energy of open strings which connect two different boundaries $a$ and $b$. Our gravity dual analysis leads to $h^{(min)}_{ab} = c/24$ for a pure AdS$_3$ gravity. This shows that a holographic boundary state is a random vector among all left-right symmetric states, whose number is given by a square root of the number of all black hole microstates. We also perform a similar computation in higher dimensions, and find that $h^{( min)}_{ab}$ depends on the tensions of the branes. In our analysis of holographic boundary states, the off diagonal elements of the inner products can be computed directly from on-shell gravity actions, as opposed to earlier calculations of inner products of microstates in two dimensional gravity.

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