Extended higher cup-Product Chern-Simons theories

Domenico Fiorenza, Hisham Sati, Urs Schreiber

Research output: Contribution to journalArticlepeer-review


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 prequantization (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.

Original languageEnglish (US)
Pages (from-to)130-163
Number of pages34
JournalJournal of Geometry and Physics
StatePublished - Dec 2013


  • Chern-Simons theory
  • Differential cohomology
  • Geometric quantization
  • M-branes
  • M-theory
  • Topological field theories

ASJC Scopus subject areas

  • Mathematical Physics
  • General Physics and Astronomy
  • Geometry and Topology


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