nLab
5d Chern-Simons theory

Context

\infty-Chern-Simons theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

Ingredients

Definition

Examples

Quantum field theory

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

higher dimensional Chern-Simons theory in dimension 5.

Properties

Moduli of fields (abelian case)

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

nnCalabi-Cau 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

References

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

Revised on May 19, 2014 01:33:55 by Urs Schreiber (217.39.7.254)