论文标题
从$ {\ cal m} $中的纠缠熵和页面曲线 - $ {
Entanglement entropy and Page curve from the ${\cal M}$-theory dual of thermal QCD above $T_c$ at intermediate coupling
论文作者
论文摘要
在中间耦合处与自上而下的非符合性全息二元双偶相关的永恒黑洞中获得页面曲线，在文献中完全没有探索。我们在中间耦合的$ t> t_c $以$ t> t_c $相关的双重全息设置的背景下填补了这一空白。值得注意的是，不包括较高的衍生术语，霍克林辐射的纠缠熵（EE），从壳上wald ee（嵌入嵌入中出现的整合常数选择适当选择）几乎随着边界时间的缘故而增加，这是由于Hartman-Maldacena（HM）$ s $ s_______________ee} β\ sim l_p^6 $。奇怪的是，这在给定时间（小于$ t_ {p} $）中赋予表面$ s_ {ee}^{hm，β^0} $的“瑞士奶酪”结构（LNS）。然后，在$ t_ {p} $之后，来自岛表面的EE贡献（IS）$ s_ {ee}^{is，β^0} $占主导地位并饱和霍金辐射的EE的线性时间增长，并导致页面曲线。需要$ s_ {ee}^{is，β^0}/s_ {bh} \ sim2 $ to在“ $ c g_n^{（11）}/r_h^9 $”的非统一形式类似物中，以及$ t_ {p} $的积极效率，以及$ t_ {p} $的积极性，分别为plose the a forme the the hore the forme the forme the forme the forem in-the-the-the-the-the-the-the-the-the-the parame $ radem $ radem ny-ny-ny-nun-inius。随着$ o（r^4）$ enter在M理论中，与HM状的表面/相关的转折点处于深度IR中，从而导致$ L_P $和$ R_H $之间的关系以及一个猜测$ e^{ - {\ cal O} β^0}/s_ {bh} \ sim2 $）。我们在$ s_ {ee}^{hm，β^0}，s_ {ee}^is，β^0}（O（β^0）$和$ s_ {ee}^ee}^{
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 $S_{EE}^{HM, β}, S_{EE}^{HM, β} (O(β))$.
