We analyze near-Hagedorn thermodynamics of strings in the WZW $AdS_3$ model. We compute the thermal spectrum of all primaries and find the thermal scalar explicitly in the string spectrum using CFT twist techniques. Then we use the link to the Euclidean WZW BTZ black hole and write down the Euclidean BTZ spectrum. We give a Hamiltonian interpretation of the thermal partition function of angular orbifolds where we find a reappearance of discrete states that dominate the partition function. Using these results, we discuss the nature of the thermal scalar in the WZW BTZ model. As a slight generalization of the angular orbifolds, we discuss the $AdS_3$ string gas with a non-zero chemical potential corresponding to angular momentum around the spatial cigar. For this model as well, we determine the thermal spectrum and the Hagedorn temperature as a function of chemical potential. Finally the nature of $α'$ corrections to the $AdS_3$ thermal scalar action is analyzed and we find the random walk behavior of highly excited strings in this particular $AdS_3$ background.
We rewrite the worldsheet torus partition function of the Thermal AdS CFT by isolating the boundary parameters. Using this, we show that the spectrum of the Euclidean BTZ black hole and Lorentzian AdS3 can be extracted -- the latter as a zero temperature limit. A similar procedure recovers the Lorentzian BTZ spectrum proposed in an earlier work. We then use our expression to construct a boundary modular invariant expression as a Poincaré series.
We study the Page curve and the information paradox for the BTZ black hole coupled to two thermal baths by applying the island paradigm. We prove that as the island locates outside the event horizon, the entanglement entropy of Hawking radiation for finite temperature black holes obeys the Page curve. However, for extremal rotating black holes, the Page time and the scrambling time become divergent. To avoid the ill-defined of the Page time, we consider the contribution of superradiance, which is a process that can extract rotational energy from black holes. The superradiance continues in a pe…
In this manuscript, we investigate the thermal properties of the rotating charged BTZ black hole under the gravity's rainbow (GR) and generalized uncertainty principle (GUP) formalism. At first, we study the GR-corrected thermal quantities according to the usual Heisenberg algebra. Then, we consider a deformed algebra that leads to a change in the Heisenberg uncertainty principle and compare the Hawking temperature, entropy, thermodynamical volume, pressure, and heat capacity functions with the previous results. Thus, we understand and interpret the quantum effects on the BTZ black hole.
We study the thermal state of a two dimensional conformal field theory which is dual to the static BTZ black hole in the high temperature limit. After partitioning the boundary of the static BTZ slice into $N$ subsystems we show that there is an underlying $C_{N-1}$ cluster algebra encoding entanglement patterns of the thermal state. We also demonstrate that the polytope encapsulating such patterns in a geometric manner for a fixed $N$ is the cyclohedron ${\mathcal C}_{N-1}$. Alternatively these patterns of entanglement can be represented in the space of geodesics (kinematic space) in terms of…
We construct a kind of thermal potential and then put the black hole thermodynamic system in it. In this regard, some thermodynamic properties of the black hole are related to the geometric characteristics of the thermal potential. Driven by the intrinsic thermodynamic fluctuations, the behavior of the black hole in the thermal potential is stochastic. With the help of solving the Fokker-Planck equation analytically, we obtain the discrete energy spectrum of Schwarzschild and Banados-Teitelboim-Zanelli (BTZ) black holes in the thermal potential. For Schwarzschild black hole, the energy spectru…
We define a generalized entanglement measure in the context of the AdS/CFT correspondence. Compared to the ordinary entanglement entropy for a spatial subregion dual to the area of the Ryu-Takayanagi surface, we take into account both entanglement between spatial degrees of freedom as well as between different fields of the boundary theory. Moreover, we resolve the contribution to the entanglement entropy of strings with different winding numbers in the bulk geometry. We then calculate this generalized entanglement measure in a thermal state dual to the BTZ black hole in the setting of the D1/…
We consider string theory on $\text{AdS}_3 \times \text{S}^3 \times \mathbb{T}^4$ in the tensionless limit, with one unit of NS-NS flux. This theory is conjectured to describe the symmetric product orbifold CFT. We consider the string on different Euclidean backgrounds such as thermal $\text{AdS}_3$, the BTZ black hole, conical defects and wormhole geometries. In simple examples we compute the full string partition function. We find it to be independent of the precise bulk geometry, but only dependent on the geometry of the conformal boundary. For example, the string partition function on ther…
Thermal Decay without Information Loss in Horizonless Microstate Geometries
我们开发了一种新的混合WKB技术来计算边界到边界的标量格林函数在渐近AdS背景中的标量波动方程是可分离的，是明确的渐近区域可解。我们将这种技术应用到一族六维$\frac{1}{8}$ -BPS渐近AdS $_3\,\times\,$ S $^3$的无视界几何中，这些几何具有与具有大视界面积的D1-D5-P黑洞相同的电荷和角动量。在大的和中等的距离，这些几何非常接近极端BTZ $\,\times\,$ S $^3$几何的黑洞，但不是有一个事件视界，这些几何有一个光滑的高度红移的全球AdS $_3\,\times\,$ S $^3$帽在IR。我们表明，响应函数的标量探测器，在动量空间，基本上由BTZ响应函数调制的高度红移的全局AdS $_3$的极点结构给出。在位置空间中，这转化为一个尖锐的指数黑洞般的衰变，时间短于$N_1 N_5$，随后出现均匀间隔的“来自帽盖的回声”，周期为$\sim N_1 N_5$。我们的结果表明，无水平微观态几何可以有相同的热衰减的黑洞没有相关的信息损失。
The black string solution is a model of black holes in (3+1) dimensions that can be related to the BTZ (2+1) dimensions black hole solution. This object can be seen as a cylindrical black hole. In this work it is considered the black string Hawking temperature obtained by the Hamilton-Jacobi method and a description of a system composed by a black string and a thermal reservoir, considering the thermal equilibrium state.
