# nLab analytically continued Chern-Simons theory

Contents

### Context

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

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

# Contents

## Idea

Where ordinary 3d Chern-Simons theory is given by an action functional with values in the circle group $\mathbb{R}/\mathbb{Z}$ on a space of special unitary group-principal connections, its “analytic continuation”(Gukov 03, Witten 10) instead is defined on complex special linear group-principal connections and its values are elements in $\mathbb{C}/\mathbb{Z}$ (see also at Chern-Simons theory with complex gauge group).

The Wilson line quantum observables of analytically continued Chern-Simons theory are accordingly analytic continuations of knot invariants (Garoufalidis 07).

## Properties

Discussion of the phase space with its complex symplectic form is in Gukov 03, section 2.2

## References

Last revised on August 13, 2015 at 16:58:49. See the history of this page for a list of all contributions to it.