Cosmological constant from condensation of defect excitations

Understand

A key challenge for many quantum gravity approaches is to construct states that describe smooth geometries on large scales.

• Here we define a family of $(2+1)$-dimensional quantum gravity states which arise from curvature excitations concentrated at point like defects and describe homogeneously curved geometries on large scales.
• These states represent therefore vacua for three-dimensional gravity with different values of the cosmological constant.
• They can be described by an anomaly-free first class constraint algebra quantized on one and the same Hilbert space for different values of the cosmological constant.