Exact Path Integral for 3D Quantum Gravity
Exact Path Integral for 3D Quantum Gravity
复制标题
3D 量子引力的精确路径积分
DOI：
10.1103/physrevlett.115.161304
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Seiji Terashima
中科院分区：
文献类型：
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作者：
Norihiro Iizuka;Akinori Tanaka;Seiji Terashima
具有负宇宙学常数的三维欧几里德纯引力可以用经典的陈-西蒙斯理论来表述。这个理论可以通过引入辅助的高吉诺和标量以超对称的方式来表达。我们使用局域化技术计算了这个Chern-Simons理论的精确配分函数。因此，我们得到了量子引力配分函数，假设它可以通过在拓扑不同的流形上对陈-西蒙斯理论的配分函数求和而非微扰地得到。由此产生的配分函数是模不变的，并且，在中心电荷预期为24的情况下，它是维滕预测的函数。
Three-dimensional Euclidean pure gravity with a negative cosmological constant can be formulated in terms of the Chern-Simons theory, classically. This theory can be written in a supersymmetric way by introducing auxiliary gauginos and scalars. We calculate the exact partition function of this Chern-Simons theory by using the localization technique. Thus, we obtain the quantum gravity partition function, assuming that it can be obtained nonperturbatively by summing over partition functions of the Chern-Simons theory on topologically different manifolds. The resultant partition function is modular invariant, and, in the case in which the central charge is expected to be 24, it is thefunction, predicted by Witten.