2025/11/26 by Liu, Tianyue, Ming, Shuang, Sun, Xin +2 · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2511.20953
In this paper, we study the asymptotics of the 6j-symbols for the principal series of the modular double of \mathrm Uq\mathfraksl(2;\mathbb R), and of their analytic extension -- what we call the b-6j symbols, relating them in various cases to the volume of truncated hyperideal tetrahedra in the hyperbolic and the anti-de Sitter geometry. To the best of our knowledge, this is the first time that the anti-de Sitter geometry appears in the asymptotics of quantum invariants. In addition, based on the connection to conformal field theory, we reveal a correspondence between the edge lengths and the dihedral angles of truncated hyperideal anti-de Sitter tetrahedra and the Fenchel-Nielsen coordinates of hyperbolic four-holed spheres. We also provide a concrete instance of 3D/2D holography, in the spirit of the AdS/CFT correspondence.