Topological Quantum Field Theory on non-Abelian gerbes

2005/10/31 by Jussi Kalkkinen
Mathematics · Physics and Astronomy · #Abelian group #Advanced Topics in Algebra #Algebraic structures and combinatorial models #BRST quantization #Cohomology #Computer science #Field (mathematics) #Gauge theory #Geometry #Homogeneous space #Homotopy and Cohomology in Algebraic Topology #Infinitesimal #Interpretation (philosophy) #Mathematical analysis #Mathematical physics #Mathematics #Nilpotent #Operator (biology) #Pure mathematics #Topological quantum field theory #hep-th

paper · pdf · doi:10.1016/j.geomphys.2006.04.003

published as J.Geom.Phys.57:505-530,2007 · 36 pages, LaTeX; v2: version to appear in J.Geom.Phys

arxiv created 2006/04/22 · openalex publication_date 2006/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The infinitesimal symmetries of a fully decomposed non-Abelian gerbe can be generated in terms of a nilpotent BRST operator, which is here constructed. The appearing fields find a natural interpretation in terms of the universal gerbe, a generalisation of the universal bundle. We comment on the construction of observables in the arising Topological Quantum Field Theory. It is also shown how the BRST operator and the trace part of a suitably truncated set of fields on the non-Abelian gerbe reduce directly to the coboundary operator and the pertinent cochains of the underlying Cech-de Rham complex.

Citations

• Non-Abelian Gerbes from Strings on a Branched Space-Time
• Quantization of Gauge Systems
• Higher Yang-Mills Theory
• Nonabelian 2-forms and loop space connections from SCFT deformations
• Non-geometric magnetic flux and crossed modules
• Gerbes, M5-Brane Anomalies and E8Gauge Theory
• Type-I D-branes in an H-flux and twisted KO-theory
• Topological quantum field theory
• Differential Geometry of Gerbes
• Combinatorial Differential Forms