Loop-Quantum-Gravity Simplicity Constraint as Surface Defect in Complex Chern-Simons Theory

Abstract

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

16 pages, 3 figures, presentation improved

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• Flux formulation of loop quantum gravity: Classical framework
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Cited by in corpus (4)

• Four-dimensional Spinfoam Quantum Gravity with Cosmological Constant: Finiteness and Semiclassical Limit
• Polysymplectic formulation for BF gravity with Immirzi parameter
• Spin foam propagator: A new perspective to include a cosmological constant
• Simplicity condition and boundary-bulk duality