# Quantum triangles and imaginary geometry flow lines

@inproceedings{Ang2022QuantumTA, title={Quantum triangles and imaginary geometry flow lines}, author={Morris Ang and Xin Sun and Pu Yu}, year={2022} }

We define a three-parameter family of random surfaces in Liouville quantum gravity (LQG) which can be viewed as the quantum version of triangles. These quantum triangles are natural in two senses. First, by our definition they produce the boundary three-point correlation functions of Liouville conformal field theory on the disk. Second, it turns out that the laws of the triangles bounded by flow lines in imaginary geometry coupled with LQG are given by these quantum triangles. In this paper we…

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