2012/07/31 by Domenico Fiorenza, Hisham Sati, Urs Schreiber
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #hep-th #math.AT #math.DG
paper · pdf · doi:10.1016/j.geomphys.2013.07.011
published as Journal of Geometry and Physics (2013), pp. 130-163 · 41 pages, exposition improved, a discussion of quadratic refinements of the bilinear forms constructed from the cup-products added. Final version
arxiv created 2013/08/07 · openalex publication_date 2013/08/08 · arxiv updated 2013/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors has a well known description: it is given on the moduli space of fields by the fiber integration of the cup product square of classes in degree-(2k+2) differential cohomology. We first refine this statement from the moduli space 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 Stringc-2-connections appearing in quantum-corrected 11-dimensional supergravity and M-branes. We discuss aspects of the off-shell extended geometric pre-quantization (in the sense of extended or multi-tiered QFT) of these theories, where there is a prequantum U(1)-k-bundle (equivalently: a U(1)-(k-1)-bundle gerbe) in each codimension k. Examples we find include moduli stacks for differential T-duality structures as well as the anomaly line bundles of higher electric/magnetic charges, such as the 5-brane charges appearing in heterotic supergravity, appearing as line bundles with connection on the smooth higher moduli stacks of field configurations.