# nLab connection on a 3-bundle

Contents

### Context

#### $\infty$-Chern-Weil theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

## Theorems

#### Differential cohomology

differential cohomology

# Contents

## Definition

For $G$ a Lie 3-group, a connection on a $G$-principal 3-bundle coming from a cocycle $g : X \to \mathbf{B}G$ is a lift of the cocycle to the 3-groupoid of Lie 3-algebra valued forms $\mathbf{B}G_{conn}$

$\array{ && \mathbf{B}G_{conn} \\ & {}^{\mathllap{\nabla}}\nearrow & \downarrow \\ X &\stackrel{g}{\to}& \mathbf{B}G }$

## References

The higher parallel transport of local 3-connections is considered in

Discussion in terms of Gray-categories is in

• Wei Wang, On 3-gauge transformations, 3-curvature and Gray-categories (arXiv:1311.3796)

Examples of 3-connections obtained from fibrations of Courant algebroids are discussed in

• Olivier Brahic, On the infinitesimal Gauge Symmetries of closed forms (arXiv)

A discussion of fully general local 3-connections is in

and the globalization is in

For a discussion of all this in a more comprehensive context see section xy of