nLab D=5 Chern-Simons theory



\infty-Chern-Simons theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory




Quantum field theory


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics



higher dimensional Chern-Simons theory in dimension 5.


Moduli of fields (abelian case)

moduli spaces of line n-bundles with connection on nn-dimensional XX

nnCalabi-Yau n-foldline n-bundlemoduli of line n-bundlesmoduli of flat/degree-0 n-bundlesArtin-Mazur formal group of deformation moduli of line n-bundlescomplex oriented cohomology theorymodular functor/self-dual higher gauge theory of higher dimensional Chern-Simons theory
n=0n = 0unit in structure sheafmultiplicative group/group of unitsformal multiplicative groupcomplex K-theory
n=1n = 1elliptic curveline bundlePicard group/Picard schemeJacobianformal Picard groupelliptic cohomology3d Chern-Simons theory/WZW model
n=2n = 2K3 surfaceline 2-bundleBrauer groupintermediate Jacobianformal Brauer groupK3 cohomology
n=3n = 3Calabi-Yau 3-foldline 3-bundleintermediate JacobianCY3 cohomology7d Chern-Simons theory/M5-brane
nnintermediate Jacobian


A general account of the structure is in

Remarks on applications in phenomemenological models are in

  • C. Hill, Physics of D=5D = 5 Chern-Simons term (pdf)

The relation to 5-dimensional supergravity is discussed in

  • A. Ceresole, A. Lerda, and P. van Nieuwenhuizen , Five-dimensional gravitational super Chern-Simons terms, Phys. Rev. D 34, 1744–1748 (1986)

  • Yuji Tachikawa, Five-dimensional Chern-Simons terms and Nekrasov’s instanton counting (arXiv:hep-th/0401184)

and via KK-compactification of the supergravity C-field of 11-dimensional supergravity in

More on supersymmetric 5d CS theory is in

  • Sergei M. Kuzenko, Joseph Novak, On supersymmetric Chern-Simons-type theories in five dimensions, JHEP 1402 (2014) 096 (arXiv:1309.6803)

See also:

Last revised on October 28, 2023 at 10:20:14. See the history of this page for a list of all contributions to it.