Two Perspectives of the 2D Unit Area Quantum Sphere and Their Equivalence
Two Perspectives of the 2D Unit Area Quantum Sphere and Their Equivalence
复制标题
二维单位面积量子球的两种视角及其等价
DOI：
10.1007/s00220-017-2979-6
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发表时间：
2015
影响因子：
2.4
通讯作者：
Xin Sun
中科院分区：
文献类型：
--
作者：
Juhan Aru;Yichao Huang;Xin Sun
二维刘维尔量子引力（LQG）是四维量子引力的玩具模型，是弦论中的世界片理论。最近，在概率论的领域中，人们对LQG的研究兴趣越来越大：大卫等人。（Liouville quantum gravity on the Riemann sphere）Commun Math Phys 342（3）：869-907，2016）和Duplantier et al.（刘维尔量子引力作为树的交配。ArXiv e-prints：arXiv：1409.7055，2014）都提供了2D球体上的LQG的概率视角。特别是，在它们中的每一个都可以找到所谓单位面积量子球的定义。我们研究这两个观点，并证明它们的等价性，表明各自的单位面积量子球是相同的。这是通过考虑一个统一的限制程序来定义两个对象。
Abstract2D Liouville quantum gravity (LQG) is used as a toy model for 4D quantum gravity and is the theory of world-sheet in string theory. Recently there has been growing interest in studying LQG in the realm of probability theory: David et al. (Liouville quantum gravity on the Riemann sphere. Commun Math Phys 342(3):869–907, 2016) and Duplantier et al. (Liouville quantum gravity as a mating of trees. ArXiv e-prints: arXiv:1409.7055, 2014) both provide a probabilistic perspective of the LQG on the 2D sphere. In particular, in each of them one may find a definition of the so-called unit area quantum sphere. We examine these two perspectives and prove their equivalence by showing that the respective unit area quantum spheres are the same. This is done by considering a unified limiting procedure for defining both objects.