Tensor network formulation of two dimensional gravity

Understand

We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant.

• More precisely the resultant continuum theory corresponds to gravity in a first-order formalism in which the local frame and spin connection are treated as independent fields.
• Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem.
• In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions.