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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 16th 2012
• (edited Jan 16th 2012)

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.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJan 16th 2012

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.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJun 20th 2015
• (edited Jun 20th 2015)

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

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeDec 20th 2017
• (edited Dec 21st 2017)

Which section of the references should this go?:

• CommentRowNumber5.
• CommentAuthorDavidRoberts
• CommentTimeDec 20th 2017

I don’t think that’s the correct link

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeDec 21st 2017

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

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeDec 21st 2017
• (edited Dec 21st 2017)

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

This deserves more discussion. But later.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeMay 1st 2018
• (edited May 1st 2018)

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.

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMar 24th 2019

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

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMar 26th 2019

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

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeMar 26th 2019

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.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeMay 30th 2019

• Sheng-Lan Ko, Dmitri Sorokin, Pichet Vanichchapongjaroen, The M5-brane action revisited, JHEP11(2013)072 (arXiv:1308.2231)
• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeJun 9th 2019

added these pointers to the list of references:

The higher WZW term of the M5-brane was maybe 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

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

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeJun 10th 2019

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)

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeJun 11th 2019
• (edited Jun 11th 2019)

• {#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 $-\tfrac{1}{6} G_4 G_4 G_4 + G_4 I_8$

• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeJun 19th 2019
• (edited Jun 19th 2019)

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
• CommentRowNumber17.
• CommentAuthorUrs
• CommentTimeJul 2nd 2019

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