nLab
holomorphic Chern-Simons theory

Contents

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

The type of field theory called holomorphic Chern-Simons theory is a variant of Chern-Simons theory where instead of Lie algebra valued differential forms on a real odd-dimensional manifold the fields are holomorphic differential forms with values in a Lie algebra on a complex odd-dimensional complex manifold, the action functional otherwise having roughly the same structure as for standard Chern-Simons theory.

Definition

See e.g. (Khesin-Wendt 08, section III 3.3)

Properties

Relation to β\beta-γ\gamma-systems

Holomorphic CS may be understood in terms of a nonabelian version of the beta-gamma system (Costello 07, section 5.3, Gwilliam, section 6.1.3).

References

Reviews include

  • Boris Khesin, Robert Wendt, section III 3.3 of The Holomorphic Chern–Simons Action Functional in The Geometry of infinite-dimensional groups, Springer 2008 (pdf)

Discussion in terms of factorization algebras of observables is in

Last revised on May 7, 2019 at 11:57:25. See the history of this page for a list of all contributions to it.