Contents

cohomology

# Contents

## Idea

The Green-Schwarz sigma-model of the M5-brane contains a 6d higher WZW term. The first summand of this term was called the Hopf-Wess-Zumino term in Intriligator 00, due to its resemblance of the Whitehead integral formula for the Hopf invariant if the C-field is assumed to be classified by a smooth function to the 4-sphere. But in fact the full term is a homotopy Whitehead integral formula (“functional cup product” or “homotopy period”) still computing the Hopf invariant if the C-field is assumed to be a cocycle in twisted cohomotopy in degree 4 (FSS 19).

Similar Hopf terms can be considered in all dimensions $4k+2$ (TN 89).

## References

The general concept of Hopf-Wess-Zumino terms was considered in

The higher WZW term of the M5-brane was first proposed in

and had been settled by the time of

The resemblence of the first summand of the term to the Whitehead integral formula for the Hopf invariant was noticed in

• Kenneth Intriligator, Anomaly Matching and a Hopf-Wess-Zumino Term in 6d, $\mathcal{N}= (2,0)$ Field Theories, Nucl. Phys. B581 (2000) 257-273 (arXiv:hep-th/0001205)

which hence introduced the terminology “Hopf-Wess-Zumino term”. Followup to this terminology includes

More on the relation to the Hopf invariant in

Discussion of the full 6d WZ term is in

Last revised on December 7, 2020 at 18:10:25. See the history of this page for a list of all contributions to it.