Speaker
Description
I discuss progress in simulating field theories on discrete hyperbolic spaces, with the goal of studying their physics in the bulk, and on the boundary. At tree-level, a free scalar field propagating in the bulk lattice is found to possess power-law two-point correlation functions on the boundary. The power-law behavior excellently matches the expected Klebanov-Witten formula despite being far away from the continuum, as well as matching the expected form due to the explicit breaking of conformal symmetry from the finite-volume boundary. When the field is dynamical---in the case of Ising spins---on a fixed hyperbolic lattice, the boundary physics is separated into two regimes depending on the bulk nearest-neighbor coupling. The conformal behavior of the free field---as well as the strong-coupling limit of the dynamical field---on the boundary can be seen explicitly to be a consequence of the hyperbolic geometry.
