论文标题
二维中黑洞蒸发的微观模型
A Microscopic Model of Black Hole Evaporation in Two Dimensions
论文作者
论文摘要
我们为SYK模型的低能能源部门偶然地介绍了黑洞（BH）“蒸发”的微观模型。为了描述蒸发，SYK模型与由$ N_F $免费标量字段$φ_i$组成的浴室耦合。我们考虑表单$ o_ {syk}（t）的耦合的线性组合\sum_iφ_i（0，t）$，其中$ o_ {syk} $涉及kourkoulou-maldacena operator $ i的产品j/n \ sum_ {k = 1}^{n/2}s'_kψ_{2k-1}（t）ψ_{2k}（t）$由spin vector $ s'$指定。我们讨论了（i）Syk系统纯状态的产品的时间演变，即以自旋矢量$ s $和有效的BH温度$ t_ {bh} $和（ii）Calabrese calabrese-cardy the PATE的特征的BH微晶格，其有效温度$ T_ {bash} $。我们采用$ t_ {bash} \ ll t_ {bh} $，而$ t_ {bh} $比SYK模型的特征UV量表$ j $低得多，从而在时间重新分析模式方面进行了描述。追踪自由度的浴室导致SYK模型的Feynman-Vernon型有效作用，我们以低能极限进行研究。找到了时间重新聚集模式的领先大型$ n $行为，以及$ o（1/\ sqrt n）$波动。后者的特征是非局部高斯噪声的非马克维亚非线性随机微分方程。在限制的耦合范围内，我们发现了两类的溶液，它们渐近地接近（a）在较低温度下的BH，以及（b）无水平的几何形状。我们分别通过部分和完整的BH蒸发来识别这些。重要的是，在这两种情况下，渐近解决方案都涉及自旋矢量$ S.S'$的标量产品，该旋转矢量$ s.s'$带有有关初始状态的一些信息。通过重复具有自旋矢量$ s'$不同选择的动态过程$ o（n^2）$ times，可以原则上重建初始BH微晶格。
We present a microscopic model of black hole (BH) `evaporation' in asymptotically $AdS_2$ spacetimes dual to the low energy sector of the SYK model. To describe evaporation, the SYK model is coupled to a bath comprising of $N_f$ free scalar fields $Φ_i$. We consider a linear combination of couplings of the form $O_{SYK}(t)\sum_iΦ_i(0,t)$, where $O_{SYK}$ involves products of the Kourkoulou-Maldacena operator $i J/N\sum_{k=1}^{N/2}s'_kψ_{2k-1}(t)ψ_{2k}(t)$ specified by a spin vector $s'$. We discuss the time evolution of a product of (i) a pure state of the SYK system, namely a BH microstate characterized by a spin vector $s$ and an effective BH temperature $T_{BH}$, and (ii) a Calabrese-Cardy state of the bath characterized by an effective temperature $T_{bath}$. We take $T_{bath}\ll T_{BH}$, and $T_{BH}$ much lower than the characteristic UV scale $J$ of the SYK model, allowing a description in terms of the time reparameterization mode. Tracing over the bath degrees of freedom leads to a Feynman-Vernon type effective action for the SYK model, which we study in the low energy limit. The leading large $N$ behaviour of the time reparameterization mode is found, as well as the $O(1/\sqrt N)$ fluctuations. The latter are characterized by a non-Markovian non-linear stochastic differential equation with non-local Gaussian noise. In a restricted range of couplings, we find two classes of solutions which asymptotically approach (a) a BH at a lower temperature, and (b) a horizonless geometry. We identify these with partial and complete BH evaporation, respectively. Importantly, the asymptotic solution in both cases involves the scalar product of the spin vectors $s.s'$, which carries some information about the initial state. By repeating the dynamical process $O(N^2)$ times with different choices of the spin vector $s'$, one can in principle reconstruct the initial BH microstate.
