标题： 从研究黑洞中的临界现象中出现的有效二维量子描述 显示英文标题

标题： The Emergence of an Effective two - dimensional Quantum Description from the study of Critical Phenomena in Black Holes

摘要： 我们研究四维旋转带电黑洞中临界现象的发生，推导出临界指数并证明它们满足标度定律。关联函数的临界指数和重整化群考虑为系统指定了一个有效（空间）维度$d=2$。对临界系统的二维高斯近似被证明可以重现黑洞的所有临界指数。讨论了更高阶的修正（总是相关的）。将二维表面与事件视界相联系，并注意到标度的推广导致共形不变性，进而导致弦理论，我们得出't Hooft对黑洞的弦解释。由此，提出了一种处理粗粒化黑洞量子化的模型。我们还给出了简单的论点，这些论点导致黑洞质量以普朗克质量为单位的粗略量子化，即$M\simeq{1\over\sqrt{2}}M_{pl} \sqrt{l}$，其中$l$是一个正整数，然后从这个结果得出量子熵与面积成正比。 显示英文摘要

摘要： We study the occurrence of critical phenomena in four - dimensional, rotating and charged black holes, derive the critical exponents and show that they fulfill the scaling laws. Correlation functions critical exponents and Renormalization Group considerations assign an effective (spatial) dimension, $d=2$, to the system. The two - dimensional Gaussian approximation to critical systems is shown to reproduce all the black hole's critical exponents. Higher order corrections (which are always relevant) are discussed. Identifying the two - dimensional surface with the event horizon and noting that generalization of scaling leads to conformal invariance and then to string theory, we arrive to 't Hooft's string interpretation of black holes. From this, a model for dealing with a coarse grained black hole quantization is proposed. We also give simple arguments that lead to a rough quantization of the black hole mass in units of the Planck mass, i. e. $M\simeq{1\over\sqrt{2}}M_{pl} \sqrt{l}$ with a $l$ positive integer and then, from this result, to the proportionality between quantum entropy and area.