Journal of High Energy Physics

, 2018:37 | Cite as

Five-dimensional fermionic Chern-Simons theory

  • Dongsu Bak
  • Andreas Gustavsson
Open Access
Regular Article - Theoretical Physics


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.


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


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Physics DepartmentUniversity of SeoulSeoulSouth Korea
  2. 2.Department of Physics and AstronomyUppsala UniversityUppsalaSweden

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