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arXiv 2207.04048hep-thgr-qc
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中间耦合下、高于 $T_c$ 的热 QCD 的 $\mathcal{M}$ 理论对偶中的纠缠熵与 Page 曲线

Entanglement entropy and Page curve from the ${\cal M}$-theory dual of thermal QCD above $T_c$ at intermediate coupling

Gopal Yadav, Aalok Misra

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AI总结：

该研究在高于 $T_c$ 的类热 QCD 的 M 理论双重全息对偶中，利用类 HM 曲面与岛曲面的纠缠熵竞争，重现 Hawking 辐射 Page 曲线，并约束视界半径及大 N 修正层级。

摘要：

在与中间耦合下自上而下的非共形全息热对偶相关的永恒黑洞背景中获得 Page 曲线，在文献中一直完全未被探索。我们在一个双重全息设置中填补了这一空白，该设置与中间耦合、$T>T_c$ 时类热 QCD 理论的 M 理论对偶相关。值得注意的是，在排除高导数项的情况下，通过在壳 Wald EE 得到的 Hawking 辐射纠缠熵（EE）（对嵌入中出现的积分常数作适当选择）几乎随边界时间线性增加，这是由于类 Hartle-Maldacena（HM）曲面 $S_{EE}^{HM,\beta^0}$ 的 EE 贡献占主导，其中 $\beta\sim l_p^6$。奇怪的是，在给定时间（小于 Page 时间 $t_P$），这使 $\mathbb{R}_{\geq0}\times\mathbb{C}$ 中的曲面 $S_{EE}^{HM,\beta^0}$ 呈现出一种“瑞士奶酪”结构，产生了可称为“大 N 情形”（LNS）的效应。随后，在 $t_P$ 之后，来自岛曲面（IS）$S_{EE}^{IS,\beta^0}$ 的 EE 贡献占据主导，并使 Hawking 辐射 EE 的线性时间增长趋于饱和，从而产生 Page 曲线。要求在非共形类比量“$cG_N^{(11)}/r_h^9$”中直至 LO 有 $S_{EE}^{IS,\beta^0}/S_{BH}\sim2$，并要求 $t_P$ 为正，分别对视界半径 $r_h$（非极端性参数）设定了下界和上界。随着 M 理论中 $O(R^4)$ 项的纳入，与类 HM 曲面/IS 相关的转折点处于深 IR，这产生了 $l_p$ 与 $r_h$ 之间的关系，以及一个推测性的 $e^{-{\cal O}(1)N^{1/3}}$ 抑制（其动机来自 $S_{EE}^{IS,\beta^0}/S_{BH}\sim2$）。我们在 $S_{EE}^{HM,\beta^0}$、$S_{EE}^{IS,\beta^0}$（$O(\beta^0)$）与 $S_{EE}^{HM,\beta}$、$S_{EE}^{HM,\beta}$（$O(\beta)$）中获得了关于这种依赖于 N 的指数的层级关系。

英文摘要：

Obtaining the Page curve in the context of eternal black holes associated with top-down non-conformal holographic thermal duals at intermediate coupling, has been entirely unexplored in the literature. We fill this gap in the context of a doubly holographic setup relevant to the M-theory dual of thermal QCD-like theories at $T>T_c$ at intermediate coupling. Remarkably, excluding the higher derivative terms, the entanglement entropy(EE) of the Hawking radiation from the on-shell Wald EE (for appropriate choices of constants of integration appearing in the embeddings) increases almost linearly with the boundary time due to dominance of EE contribution from the Hartman-Maldacena(HM)-like surface $S_{EE}^{HM, β^0}, β\sim l_p^6$. Curiously, this imparts a "Swiss-Cheese" structure to the surface $S_{EE}^{HM, β^0}$ at a given time (less than the Page time $t_{P}$), in $\mathbb{R}_{\geq0} \times \mathbb{C}$ effecting what could be dubbed as a "Large N Scenario" (LNS). Then, after $t_{P}$, the EE contribution from the Island Surface (IS) $S_{EE}^{IS, β^0}$ dominates and saturates the linear time growth of the EE of Hawking radiation and leads to the Page curve. Requiring $S_{EE}^{IS, β^0}/S_{BH}\sim2$ up to LO in the non-conformal analog of "$c G_N^{(11)}/r_h^9$", and positivity of $t_{P}$, set respectively a lower and upper bound on the horizon radius $r_h$ (the non-extremality parameter). With the inclusion of the $O(R^4)$ terms in M theory, the turning point associated with the HM-like surface/IS being in the deep IR, results in a relationship between $l_p$ and $r_h$ along with a conjectural $e^{-{\cal O}(1) N^{1/3}}$-suppression (motivated by $S_{EE}^{IS, β^0}/S_{BH}\sim2$). We obtain a hierarchy with respect to this N-dependent exponential in $S_{EE}^{HM, β^0}, S_{EE}^{IS, β^0} (O(β^0))$ and $S_{EE}^{HM, β}, S_{EE}^{HM, β} (O(β))$.

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