Scalar fields on fluctuating hyperbolic geometries

Understand

We present results on the behavior of the boundary-boundary correlation function of scalar fields propagating on discrete two-dimensional random triangulations representing manifolds with the topology of a disk.

• We use a gravitational action that includes a curvature squared operator, which favors a regular tessellation of hyperbolic space for large values of its coupling.
• We probe the resultant geometry by analyzing the propagator of a massive scalar field and show that the conformal behavior seen in the uniform hyperbolic space survives as the coupling approaches zero.
• The analysis of the boundary correlator suggests that holographic predictions survive, at least, weak quantum gravity corrections.