this pointer to one of the original references had been missing:

- Paul Howe, Ergin Sezgin, Peter West,
*Covariant Field Equations of the M Theory Five-Brane*, Phys. Lett. B399 (1997) 49-59 (arXiv:hep-th/9702008)

added more of the original references, such as the non-covariant pre-cursors of the self-duality mechanism in

- John Schwarz,
*Coupling a Self-Dual Tensor to Gravity in Six Dimensions*, Phys.Lett.B395:191-195,1997

added pointer to

- {#BBMN19} Ibrahima Bah, Federico Bonetti, Ruben Minasian, Emily Nardoni,
*Anomaly Inflow for M5-branes on Punctured Riemann Surfaces*(arXiv:1904.07250)

which gives/recalls an(other) argument for the full anomaly inflow 12-form being all of $-\tfrac{1}{6} G_4 G_4 G_4 + G_4 I_8$

]]>further on the Hopf-WZ term: added also pointer to

Jussi Kalkkinen, Kellogg Stelle, Section 3.2 of:

*Large Gauge Transformations in M-theory*, J. Geom. Phys. 48 (2003) 100-132 (arXiv:hep-th/0212081)Alex Arvanitakis, Section 4.1 of:

*Brane Wess-Zumino terms from AKSZ and exceptional generalised geometry as an $L_\infty$-algebroid*(arXiv:1804.07303)

added these pointers to the list of references:

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

- Ofer Aharony, p. 11 of
*String theory dualities from M theory*, Nucl. Phys. B476:470-483, 1996 (arXiv:hep-th/9604103)

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, 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

- Shan Hu, Dimitri Nanopoulos,
*Hopf-Wess-Zumino term in the effective action of the 6d, (2, 0) field theory revisted*, JHEP 1110:054, 2011 (arXiv:1110.0861)

More on the relation to the Hopf invariant in

- Hisham Sati,
*Framed M-branes, corners, and topological invariants*, J. Math. Phys. 59 (2018), 062304 (arXiv:1310.1060)

added pointer to

- Sheng-Lan Ko, Dmitri Sorokin, Pichet Vanichchapongjaroen,
*The M5-brane action revisited*, JHEP11(2013)072 (arXiv:1308.2231)

I don’t understand that the term $G_W^2$ in (3.7) of arXiv:1310.2250 should be there.

I understand that in non-rational cohomology there is an extra torsion contribution on top of $L$, and that’s discussed in section 4 of arXiv:1110.4639. But in rational cohomology there should just remain the $L$-term in that (3.7), and then, it seems to me, there is lacking a condition/reason for the term with $G_W^2$ to vanish in rational cohomology.

]]>highlighted another subtlety in the computation of the M5 anomaly cancellation, and added further pointers to the literature (same edits also at I8)

]]>added a section on anomaly cancellation (here) – currently this is identical with the corresponding section at *I8*, just copied over

added pointer to Witten 95, about identifying the $\mathcal{N} =(2,0)$ black M5 at a transversal $\mathbb{R}^5 \sslash \mathbb{Z}_2$-orbifold singularitiy.

Removed the pointer to section 8.3 of “Half-BPS M2-brane orbifolds”. Closer inspection shows that the thing classified there is really the MK6, not the M5. I’ll give more details on the subtleties in a few days.

]]>I have added it to the end of *References – Worldvolume theory*.

This deserves more discussion. But later.

]]>Oh yes, thanks, I’ve changed it to the right one.

]]>I don’t think that’s the correct link

]]>Which section of the references should this go?:

- Christian Saemann, Lennart Schmidt,
*An M5-Brane Model*, (arXiv:1712.06623)

With Domenico Fiorenza and Hisham Sati we are finalizing a note on *The WZW term of the M5-brane (schreiber)*.

I have now added the discussion of this effect more generally to the entry higher dimensional Chern-Simons theory in a new subsection *Background charges and square root action functionals*.

I have added to *M5-brane* a fairly detailed discussion of the issue with the fractional quadratic form on differential cohomology for the dual 7d-Chern-Simons theory action (from Witten (1996) with help of Hopkins-Singer (2005)).

In the new section *Conformal blocks and 7d Chern-Simons dual*.