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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.
added pointer to
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
More on the relation to the Hopf invariant in
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 pointer to
which gives/recalls an(other) argument for the full anomaly inflow 12-form being all of $-\tfrac{1}{6} G_4 G_4 G_4 + G_4 I_8$
added more of the original references, such as the non-covariant pre-cursors of the self-duality mechanism in
this pointer to one of the original references had been missing:
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