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Hyperbolicity of partition function and quantum gravity. (English) Zbl 1020.83015

Summary: We study a geometry of the partition function which is defined in terms of a solution of the five-term relation. It is shown that the 3-dimensional hyperbolic structure or the Euclidean \(\text{AdS}_3\) naturally arises in the classical limit of this invariant. We discuss that the oriented ideal tetrahedron can be assigned to the partition function of string.

MSC:

83C45 Quantization of the gravitational field
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