Quantum graphity: a model of emergent locality in quantum gravity

          @misc{ pirsa_PIRSA:09030018,
            doi = {10.48660/09030018},
            url = {https://pirsa.org/09030018},
            author = {},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Quantum graphity: a model of emergent locality in quantum gravity},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {mar},
            note = {PIRSA:09030018 see, \url{https://pirsa.org}}
          }
          

Abstract

Quantum graphity is a background independent condensed matter model for emergent locality, spatial geometry and matter in quantum gravity. The states of the system are given by bosonic degrees of freedom on a dynamical graph on N vertices. At high energy, the graph is the complete graph on N vertices and the physics is invariant under the full symmetric group acting on the vertices and highly non-local. The ground state dynamically breaks the permutation symmetry to translations and rotations. In this phase the system is ordered, low-dimensional and local. The model gives rise to an emergent U(1) gauge theory in the ground state by the string-net condensation mechanism of Levin and Wen. In addition, in such a model, observable effects of emergent locality such as its imprint on the CMB can be studied. Finding the right dynamics for the desired ground state is ongoing work and I will review some of the basic results with an emphasis on the use of methods from quantum information theory such as topological order and the use of the Lieb-Robinson bounds to find the speed of light in the system.