A Higher Stacky Perspective on Chern–Simons Theory

Domenico Fiorenza, Hisham Sati, Urs Schreiber

Research output: Chapter in Book/Report/Conference proceedingChapter


The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern–Simons-type gauge field theories. We explain in some detail how the action functional of ordinary 3d Chern–Simons theory is naturally localized (“extended”, “multi-tiered”) to a map on the universal moduli stack of principal connections, a map that itself modulates a circle-principal 3-connection on that moduli stack, and how the iterated transgressions of this extended Lagrangian unify the action functional with its prequantum bundle and with the WZW-functional. In the second part we provide a brief review and outlook of the higher prequantum field theory of which this is a first example. This includes a higher geometric description of supersymmetric Chern–Simons theory, Wilson loops and other defects, generalized geometry, higher Spin-structures, anomaly cancellation, and various other aspects of quantum field theory.

Original languageEnglish (US)
Title of host publicationMathematical Physics Studies
Number of pages59
StatePublished - 2015

Publication series

NameMathematical Physics Studies
VolumePart F1113
ISSN (Print)0921-3767
ISSN (Electronic)2352-3905


  • Chern-Simons Theory
  • Differential Purification
  • Homotopy Pullback
  • Moduli Stack
  • Prequantum Bundle

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Statistical and Nonlinear Physics


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