nLab
Courant sigma-model

Context

\infty-Chern-Simons theory

Ingredients

Definition

Examples

  • For targets

  • For targets

  • For discrete targets

  • For targets

    • coupled to
  • For targets extending the

    (such as the , the )

    • Chern-Simons-

  • for higher abelian targets

  • for targets

        • ,
  • for the L L_\infty-structure on the of the closed :

Quantum field theory

Contents

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  • FQFT and

Physics

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Surveys, textbooks and lecture notes

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      • and
    • Axiomatizations

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        • -theorem

    • Tools

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    • Structural phenomena

    • Types of quantum field thories

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        • examples

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Contents

Idea

Every symplectic Lie n-algebroid (𝔓,ω)(\mathfrak{P},\omega) carries a specified invariant polynomial ω\omega. The action functional induced by the corresponding Chern-Simons element in ∞-Chern-Simons theory defined the corresponding AKSZ theory sigma model.

For a Courant algebroid (𝔓,ω)(\mathfrak{P}, \omega) this is called the Courant σ\sigma-model .

from binary and non-degenerate

nn \in \mathbb{N} = of of (n+1)(n+1)-d (n+1)(n+1)d / = of in (n+1)(n+1)discussed in:
0ordinary
1 (of underlying )brane of Poisson sigma-model = over
2 in
nnd=n+1d = n+1

(adapted from )

References

The action functional was first deduced in

As an example of an AKSZ sigma-model it was later re-derived in

Further discussion is in

The interpretation in terms of infinity-Chern-Weil theory is discussed in

Relations to generalized complex geometry is discussed in

Last revised on February 8, 2013 at 02:09:04. See the history of this page for a list of all contributions to it.