Loop quantum gravity simplicity constraint as surface defect in complex Chern-Simons theory

摘要

The simplicity constraint is studied in the context of four-dimensional spinfoam models with a cosmological constant. We find that the quantum simplicity constraint is realized as the two-dimensional surface defect in SL(2,C) Chern-Simons theory in the construction of spinfoam amplitudes. By this realization of the simplicity constraint in Chern-Simons theory, we are able to construct the new spinfoam amplitude with a cosmological constant for an arbitrary simplicial complex (with many 4-simplices). The semiclassical asymptotics of the amplitude is shown to correctly reproduce the four-dimensional Einstein-Regge action with a cosmological constant term.