nLab
analytically continued 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

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.