Abstract:

I will discuss progress in the programme of establishing a holographic duality for regular tilings of hyperbolic space. As candidate boundary theories, we consider spin chains with aperiodic couplings whose ground state may be represented by a tensor network. Moreover, we consider Majorana spin chains that explicitly realize transitions between von Neumann algebras recently considered in view of understanding black hole Hilbert spaces. On the bulk side, we consider discretizations of JT gravity that may be mapped to an Ising model of which we calculate the spectral function. The work is motivated in part by recent developments in condensed matter physics on hyperbolic tilings and their experimental realizations.