Topological order of quantum gravity in AdS3 spacetime

Topological order is a new type of order that beyond Landau’s symmetry-breaking theory. It has some interesting properties, such as producing quasi-particles with fractional quantum numbers and fractional/Fermi statistics, robust gapless bound-ary modes, and emergent gauge excitations. In this paper, we will show that the quan-tum gravity in AdS3 spacetime can also have topological orders. Actually, the theory has all the three features that define the topological order. We conjecture that quantum gravity in four dimensions can also have topological orders.