Abstract

A “Σ-model ” can be thought of as a quantum field theory (QFT) which is determined by pulling back n-bundles with connection (aka (n−1)-gerbes with connection, aka nonabelian differential cocycles) along all possible maps (the “fields”) from a “parameter space ” to the given base space. If formulated suitably, such Σ-models include gauge theories such as notably (higher) Chern-Simons theory. If the resulting QFT is considered as an “extended ” QFT, it should itself be a nonabelian differential cocycle on parameter space whose parallel transport along pieces of parameter space encodes the QFT propagation and correlators. We are after a conception of nonabelian differential cocycles and their quantization which captures this. Our main motivation is the quantization of differential Chern-Simons cocycles to extended Chern-Simons QFT and its boundary conformal QFT, reproducing the cocycle structure implicit in [23]. • Classical – We conceive nonabelian differential cohomology in terms of cohomology with coefficients in ω-category-valued presheaves [48] of parallel transport ω-functors from ω-paths to a given

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