Topological Order of Quantum Gravity in $AdS_3$ Spacetime

TL;DR

This paper explores the presence of topological order in quantum gravity within $AdS_3$ spacetime, highlighting its properties and proposing its potential existence in higher dimensions.

Contribution

It demonstrates that quantum gravity in $AdS_3$ can exhibit topological order, a novel perspective linking quantum gravity and topological phases.

Findings

Quantum gravity in $AdS_3$$ exhibits topological order features.

The theory shows fractional quantum numbers and emergent gauge excitations.

Conjecture that 4D quantum gravity may also have topological order.

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.