nLab infinity-Chern-Simons theory - contents

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

Ingredients

• quantum field theory

• circle n-bundle with connection

• ∞-Chern-Weil theory

  • ∞-Lie algebroid cohomology

  • Chern-Simons element

Definition

• level (Chern-Simons theory)

Examples

• For semisimple Lie algebra targets

  • Chern-Simons theory

• For discrete group targets

  • Dijkgraaf-Witten theory

• For discrete 2-group targets

  • Crane-Yetter model

• For Lie 2-algebra targets

  • BF-theory coupled to topological Yang-Mills theory

• For targets extending the super Poincare Lie algebra

  (such as the supergravity Lie 3-algebra, the supergravity Lie 6-algebra)

  • Chern-Simons gravity

  • Chern-Simons-supergravity

• 1-dimensional Chern-Simons theory

• for higher abelian targets

  • higher dimensional Chern-Simons theory

  • higher electric background charge coupling

• for symplectic Lie n-algebroid targets

  • AKSZ theory

    • Poisson sigma model

      • A-model, B-model

    • Courant sigma model

      • Chern-Simons theory

    • topological Yang-Mills theory

• for the $L_\infty$-structure on the BRST complex of the closed string:

  • string field theory

• higher dimensional Chern-Simons theory

  • 1d Chern-Simons theory

    • Wilson loop

  • 2d Chern-Simons theory

    • Poisson sigma-model,

    • A-model, B-model topological string

  • 3d Chern-Simons theory

    • Chern-Simons theory

    • Dijkgraaf-Witten theory

    • Courant sigma-model

    • 3d quantum gravity

  • 4d Chern-Simons theory

    • Yetter model

    • BF-theory

  • 5d Chern-Simons theory

  • 6d Chern-Simons theory

  • 7d Chern-Simons theory

    • topological AdS7/CFT6-sector

    • topological M-theory

  • 11d Chern-Simons theory

    • RR-field

• ∞-Chern-Simons theory

  • ∞-Dijkgraaf-Witten theory

  • string field theory

  • AKSZ sigma-model