# nLab Chern-Simons theory as topological string theory

Contents

### Context

#### Duality in string theory

duality in string theory

general mechanisms

string-fivebrane duality

string-string dualities

M-theory

F-theory

string-QFT duality

QFT-QFT duality:

# Contents

## Idea

Under mapping the Feynman diagrams of perturbative Chern-Simons theory on a 3-manifold $X^3$ via 't Hooft double line notation to open string worldsheets, its quantum observables (Wilson loop Vassiliev knot invariants) are equivalent to those of an open topological string theory with target space the cotangent bundle $T^\ast X^3$ with D3-branes. (Witten 92)

For $X^3 = S^3$ the 3-sphere, the large N limit is also dual, in a topological string/TQFT-version of AdS/CFT duality, to a closed topological string theory with target space the blow-up of the conifold (Gopakumar-Vafa 98).

## References

Review:

### Direct open topological string theory

The original article:

### Dual closed topological string theory

Including Wilson loop observables:

Last revised on January 7, 2020 at 18:10:28. See the history of this page for a list of all contributions to it.