复Chern-Simons理论中作为表面缺陷的圈-量子引力简单性约束
Loop-Quantum-Gravity Simplicity Constraint as Surface Defect in Complex Chern-Simons Theory
摘要：
研究了具有宇宙学常数的四维自旋泡沫模型的简单性约束。我们发现，在构造自旋泡沫振幅时，SL（2，$\mathbb{C}$）Chern-Simons理论中的量子简单性约束是通过二维表面缺陷实现的.通过实现Chern-Simons理论中的单纯性约束，我们可以构造出任意单纯复形（有许多4-单纯形）的具有宇宙学常数的自旋泡沫振幅.振幅的半经典渐近性正确地再现了具有宇宙学常数项的四维Einstein-Regge作用量。
英文摘要：
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.
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