2025/06/06 by Hank Chen, Chen, Hank · 1 citation
Mathematics · #20G42 #57K45 #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2506.05785
openalex publication_date 2025/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a continuation of the first paper (arXiv:2501.06486) of this series, where the framework for the combinatorial quantization of the 4d 2-Chern-Simons theory with an underlying compact structure Lie 2-group \mathbbG was laid out. In this paper, we continue our quest and characterize additive module *-functors ω:\mathfrakCq(\mathbbGΓ2)\rightarrowHilb, which serve as a categorification of linear *-functionals (ie. a state) on a C^*-algebra. These allow us to construct non-Abelian Wilson surface correlations \widehat\mathfrakCq(\mathbbGP) on the discrete 2d simple polyhedra P partitioning 3-manifolds. By proving its stable equivalence under 3d handlebody moves, these Wilson surface states extend to decorated 3-dimensional marked bordisms in a 4-disc D4. This provides invariants of framed oriented 2-ribbonsin D4 from the data of the given compact Lie 2-group \mathbbG. We find that these 2-Chern-Simons-type 2-ribbon invariants are given by bigraded ℤ-modules, similar to the lasagna skein modules of Manolescu-Walker-Wedrich.