An article that we have written:
Extended higher cup-product Chern-Simons theories
Journal of Geometry and Physics
Volume 74, 2013, Pages 130–163
Abstract. It is well known that the proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors is given on gauge equivalence classes of gauge fields by the fiber integration of the cup product square of classes in degree- differential cohomology.
We first refine this statement from gauge equivalence classes to the full higher smooth moduli stack of fields, to which the higher-order-ghost BRST complex is the infinitesimal approximation. Then we generalize the refined formulation to cup product Chern-Simons theories of nonabelian and higher nonabelian gauge fields, such as the nonabelian String 2-connections appearing in quantum-corrected 11-dimensional supergravity (FSSa, FSSb).
We discuss aspects of the off-shell extended geometric quantization (in the sense of extended or multi-tiered QFT) of these theories (FRS), with prequantum circle k-bundles (-bundle gerbes) in each codimension .
Extended higher cup product Chern-Simons theories