Topological Order of Quantum Gravity in $AdS_3$ Spacetime

Abstract

Topological order is a new type 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 boundary modes and emergent gauge excitations. In this essay, we will show that the quantum gravity in $AdS_3$ 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 dimension can also have topological orders.