Scalar fields on fluctuating hyperbolic geometry

We investigate a model consisting of Kahler-Dirac fermions propagating on discrete triangulations of a negatively curved disk. After integrating out massive fermions we show that the effective discrete gravity action picks up curvature terms. For a large number of fermion flavors, we show that the geometry

approaches a fixed regular tessellation of two dimensional hyperbolic geometry. In this limit, we observe power law boundary correlation functions

consistent with holography. Using Monte Carlo we investigate if there is a transition to a non-holographic phase as a function of the fermion mass and

number of flavors.