论文标题
在弦理论中的小黑洞上
On Small Black Holes in String Theory
论文作者
论文摘要
我们讨论了世界表格的Sigma-Model，其目标空间是$ D+1 $尺寸的Euclidean Schwarzschild Black Hole。我们认为，在限制下，黑洞的鹰温度（$ t $）接近Hagedorn温度，$ T_H $，可以用Horowitz-Polchinski有效理论的广义版本来描述。对于$ d \ geq6 $，horowitz-polchinski eft [1,2]没有合适的解决方案，修改后的有效拉格朗日人允许人们在扩展$ d-6 $ and $ t_h-t $的扩展中研究黑洞CFT。在$ t = t_h $时，Sigma模型对于所有$ d> 6 $都是不平凡的。它表现出增强的$ su（2）$对称性，并通过具有径向依赖的耦合的非亚洲斜视模型来描述。所得图片与[3-5]的结果自然相关，该结果将schwarzschild的黑洞与$ d $大的时空中的黑洞与二维黑洞相关联。我们还讨论了一个类似的开放式弦系统，其中黑洞被两个通过喉咙连接的两个分离的D-Branes的系统取代。在该系统中，渐近分离晶体起着反向温度的作用。在临界分离时，系统由近托型模型描述，该模型再次表现出增强的$ su（2）$对称性。在$ d $的大致上，勃雷系统产生了发夹brane [6]。
We discuss the worldsheet sigma-model whose target space is the $d+1$ dimensional Euclidean Schwarzschild black hole. We argue that in the limit where the Hawking temperature of the black hole, $T$, approaches the Hagedorn temperature, $T_H$, it can be described in terms of a generalized version of the Horowitz-Polchinski effective theory. For $d\geq6$, where the Horowitz-Polchinski EFT [1,2] does not have suitable solutions, the modified effective Lagrangian allows one to study the black hole CFT in an expansion in powers of $d-6$ and $T_H-T$. At $T=T_H$, the sigma model is non-trivial for all $d>6$. It exhibits an enhanced $SU(2)$ symmetry, and is described by a non-abelian Thirring model with a radially dependent coupling. The resulting picture connects naturally to the results of [3-5], that relate Schwarzschild black holes in flat spacetime at large $d$ to the two dimensional black hole. We also discuss an analogous open string system, in which the black hole is replaced by a system of two separated D-branes connected by a throat. In this system, the asymptotic separation of the branes plays the role of the inverse temperature. At the critical separation, the system is described by a Kondo-type model, which again exhibits an enhanced $SU(2)$ symmetry. At large $d$, the brane system gives rise to the hairpin brane [6].
