Five-dimensional fermionic Chern-Simons theory

Dongsu Bak, Andreas Gustavsson

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2 Scopus citations


We study 5d fermionic CS theory with a fermionic 2-form gauge potential. This theory can be obtained from 5d maximally supersymmetric YM theory by performing the maximal topological twist. We put the theory on a five-manifold and compute the partition function. We find that it is a topological quantity, which involves the Ray-Singer torsion of the five-manifold. For abelian gauge group we consider the uplift to the 6d theory and find a mismatch between the 5d partition function and the 6d index, due to the nontrivial dimensional reduction of a selfdual two-form gauge field on a circle. We also discuss an application of the 5d theory to generalized knots made of 2d sheets embedded in 5d.

Original languageEnglish
Article number37
JournalJournal of High Energy Physics
Issue number2
StatePublished - 1 Feb 2018


  • BRST Quantization
  • Field Theories in Higher Dimensions
  • Supersymmetric Gauge Theory
  • Topological Field Theories


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