Five-dimensional fermionic Chern-Simons theory
- 47 Downloads
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.
KeywordsBRST Quantization Field Theories in Higher Dimensions Supersymmetric Gauge Theory Topological Field Theories
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- J-H. Park and N. Nekrasov, private notes.Google Scholar
- D.B Ray, Reidemeister torsion and the laplacian on lens spaces, Adv. Math. 4 (1970) 109.Google Scholar
- U. Bunke, Lectures on analytic torsion, http://www.uni-regensburg.de/Fakultaeten/nat Fak I/Bunke/sixtorsion.pdf.
- P.A. Kirk and E.P. Klassen, Chern-Simons invariants of 3-manifolds and representation spaces of knot groups, Math. Ann. 287 (1990) 343, http://eudml.org/doc/164690.