2-Chern-Simons theory, or more commonly known as 4d BF-BB theory with gauged shift symmetry, is a natural generalization of Chern-Simons theory to 4-dimensional manifolds. It is part of the bestiary of higher-dimensional AKSZ/homotopy Maurer-Cartan theories. In this talk, I will present a framework towards the combinatorial quantization of 2-Chern-Simons theory on the lattice, taking inspiration from the work of Aleskeev-Grosse-Schomerus three decades ago. From the 2-categorical model for the higher holonomies and their 2-gauge transformations, I will introduce their correpsonding states in a sheaf-theoretic framework based on Crane-Yetter's measureable categories, as well as their deformation quantization. This leads to an explicit realization of the higher 2-tangle hypothesis of Baez-Langford, and also provides insight into the (non-perturbative) quantization of derived AKSZ theories in general.
Brief bio: Hank Chen is currently a postoc at BIMSA/Tsinghua YMSC specializing in mathematical physics, with interest in 4d TQFTs, higher categorical algebras and integrability. He completed his PhD at the University of Waterloo/Perimeter Institute in 2024, studying quantum group Hopf algebras and their higher homotopy generalizations.
Tencent Meeting：614-272-585
Prof. Yinan Wang