Complex Chern-Simons theory with k=8N and an improved spinfoam model with a cosmological constant
Han M, Pan Q (2025)
Publication Type: Journal article
Publication year: 2025
Journal
Book Volume: 112
Pages Range: 01-25
Journal Issue: 2
DOI: 10.1103/pkt7-sv9r
Abstract
This paper presents an improvement to the four-dimensional spinfoam model with cosmological constant (Λ-SF model) in loop quantum gravity. The original Λ-SF model, defined via SLð2;CÞ Chern-Simons theory on graph-complement 3-manifolds, produces finite amplitudes and reproduces curved 4-simplex geometries in the semiclassical limit. However, extending the model to general simplicial complexes necessitated ad hoc, nonuniversal phase factors in face amplitudes, complicating systematic constructions. We resolve this issue by redefining the vertex amplitude using a novel set of phase space coordinates that eliminate the extraneous phase factor, yielding a universally defined face amplitude. Key results include: (1) The vertex amplitude is rigorously shown to be well defined for Chern-Simons levels k∈ 8N, compatible with semiclassical analysis (k → ∞). (2) The symplectic structure of the Chern-Simons phase space is modified to accommodate SLð2;CÞ holonomies, relaxing quantization constraints to Spð2r;Z=4Þ. (3) Edge amplitudes are simplified using constraints aligned with colored tensor models, enabling systematic gluing of 4-simplices into complexes dual to colored graphs. (4) Stationary phase analysis confirms consistency of critical points with prior work, recovering Regge geometries with curvature determined by Λ. These advancements streamline the spinfoam amplitude definition, facilitating future studies of colored group field theories and continuum limits of quantum gravity. The results establish a robust framework for 4D quantum gravity with nonzero Λ, free of previous ambiguities in face amplitudes.
Involved external institutions
United States (USA) (US)How to cite
APA:
Han, M., & Pan, Q. (2025). Complex Chern-Simons theory with k=8N and an improved spinfoam model with a cosmological constant. Physical Review D, 112(2), 01-25. https://doi.org/10.1103/pkt7-sv9r
MLA:
Han, Muxin, and Qiaoyin Pan. "Complex Chern-Simons theory with k=8N and an improved spinfoam model with a cosmological constant." Physical Review D 112.2 (2025): 01-25.
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