Holographic Space-time Models in $1 + 1$ Dimensions
Holographic Space-time Models in $1 + 1$ Dimensions
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1 美元 1 美元维度的全息时空模型
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发表时间：
2015
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通讯作者：
Tom Banks
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作者：
Tom Banks
我们构建全息时空模型，再现了1 + 1$维弦理论的动力学。在经典几何的1 + 1$有效拉格朗日量中，费米子场的必要性，费米子的出现，甚至在正则1 $矩阵模型中的普适势的形式，都来自一般的HST考虑。我们注意到，t Hooft的anademic的主要贡献的黑洞S-矩阵，占整个S-矩阵在这些模型中的限制，弦尺度符合普朗克尺度，近视界和渐近坐标之间的转换。这些1 + 1维模型可以描述为高维极端黑洞或黑膜的近视界几何的解耦极限，这表明最简单模型的变形同样是物理的。在提出了“相关变形”的概念后，我们描述了变形，其中包含对应于线性黑洞的激发，其中一些可以被认为是CGHS模型的UV完成。我们研究的问题是否AMPS悖论可以制定在这些模型。这是不可能的，因为到线性双光子黑洞奇点的经典落入时间与黑洞质量无关。我们的HST模型再现了这一结果。我们认为这与黑洞解的准正规模的缺乏有关，而准正规模的缺乏又与视界面积为零有关。这是兼容的解决方案提出的AMPS悖论在以前的工作与Fischler，根据该兼容性条件的HST确定长期的非奇异逗留的观察员背后的地平线，动态平衡的地平线上看到的检测器尚未通过地平线下降。
We construct Holographic Space-time models that reproduce the dynamics of $1 + 1$ dimensional string theory. The necessity for a dilaton field in the $1 + 1$ effective Lagrangian for classical geometry, the appearance of fermions, and even the form of the universal potential in the canonical $1$ matrix model, follow from general HST considerations. We note that 't Hooft's ansatz for the leading contribution to the black hole S-matrix, accounts for the entire S-matrix in these models in the limit that the string scale coincides with the Planck scale, up to transformations between near horizon and asymptotic coordinates. These $1 + 1$ dimensional models are describable as decoupling limits of the near horizon geometry of higher dimensional extremal black holes or black branes, and this suggests that deformations of the simplest model are equally physical. After proposing a notion of "relevant deformations", we describe deformations, which contain excitations corresponding to linear dilaton black holes, some of which can be considered as UV completions of the CGHS model. We study the question of whether the AMPS paradox can be formulated in those models. It cannot, because the classical in-fall time to the singularity of linear dilaton black holes, is independent of the black hole mass. This result is reproduced by our HST models. We argue that it is related to the absence of quasi-normal modes of these black hole solutions, which is itself related to the fact that the horizon has zero area. This is compatible with the resolution of the AMPS paradox proposed in previous work with Fischler, according to which the compatibility conditions of HST identify the long non-singular sojourn of observers behind the horizon, with the dynamics of equilibration on the horizon as seen by a detector which has not yet fallen through the horizon.