Quantum flatness in twodimensional quantum gravity
Abstract
Flatness—the absence of spacetime curvature—is a wellunderstood property of macroscopic, classical spacetimes in general relativity. The same cannot be said about the concepts of curvature and flatness in nonperturbative quantum gravity, where the microscopic structure of spacetime is not describable in terms of small fluctuations around a fixed background geometry. An interesting case is given by the twodimensional models of quantum gravity, which lack a classical limit and therefore are maximally "quantum." We investigate the recently introduced quantum Ricci curvature in causal dynamical triangulations quantum gravity on a twodimensional torus, whose quantum geometry could be expected to behave as a flat space on suitably coarsegrained scales. On the basis of Monte Carlo simulations we have performed, with system sizes of up to 600.000 building blocks, this does not seem to be the case. Instead, we find a scaleindependent "quantum flatness," without an obvious classical analog. As part of our study, we develop a criterion that allows us to distinguish between local and global topological properties of the toroidal quantum system.
 Publication:

Physical Review D
 Pub Date:
 December 2021
 DOI:
 10.1103/PhysRevD.104.126024
 arXiv:
 arXiv:2110.11100
 Bibcode:
 2021PhRvD.104l6024B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Lattice
 EPrint:
 33 pages,16 figures