SIMIS Seminar series on Random matrix theory, Integrable systems and Applications: Combinatorial quantization of 4-dimensional higher-Chern-Simons theory

Speaker: Dr. Hank Chen (BIMSA)

Time: Wednesday 20th August 2025, 14:00h-15:00h
Location: Room: 1610, SIMIS
Zoom Meeting ID:834 2013 4183 (Passcode:SIMIS)

Abstract
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. I will introduce the notion of Crane-Yetter’s measureable fields, with which one can model states of higher holonomies in 2-Chern-Simons theory. This leads to an explicit realization of the categorical ladder proposal of Baez-Dolan, and also provides insight into the non-perturbative quantization of higher-AKSZ theories in general.