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arXiv · 2501.17930

Conformal Dimensions On Causal Random Geometry

Ryan Barouki·Henry Stubbs·John Wheater
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Abstract

We investigate the interaction between matter and causal dynamical triangulations (CDT) in the context of two-dimensional quantum gravity. We focus on the Ising model coupled to CDT, contrasting this with Liouville gravity and the relation to the Knizhnik-Polyakov-Zamolodchikov (KPZ) formula. We demonstrate analytically for the quenched model that the conformal dimensions of fields on CDT align with those on a fixed lattice. We do this using a combination of lattice methods and adapting the Duplantier-Sheffield framework to CDT, emphasizing the one-dimensional nature of CDT and its description via a stochastic differential equation.

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Ryan Barouki, Henry Stubbs, John Wheater. 2025-01-29. Conformal Dimensions On Causal Random Geometry. https://doi.org/10.1007/jhep07(2025)173

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