# nLab holomorphic Chern-Simons theory

Contents

### Context

#### $\infty$-Chern-Simons theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

# 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 $\beta$-$\gamma$-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.