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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.
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.
With Domenico Fiorenza and Hisham Sati we are finalizing a note on The WZW term of the M5-brane (schreiber).
Which section of the references should this go?:
I don’t think that’s the correct link
Oh yes, thanks, I’ve changed it to the right one.
I have added it to the end of References – Worldvolume theory.
This deserves more discussion. But later.
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 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.
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