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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:
took the liberty of pointing to our article today
for cancellation of the remaining M5 anomaly term via Hypothesis H
added DOI to
added pointer to:
and
and added to the discussion of the remaining anomaly term here the remark that and where these authors agree that the basic form component to $G_4$ needs to be considered.
looking at the preprint dates, I am taking the liberty of clarifying the order of events, by including pointer to version 1 of our FSS19, as follows:
{#FSS19v1} Domenico Fiorenza, Hisham Sati, Urs Schreiber, around equation (19) in: Twisted Cohomotopy implies M-Theory anomaly cancellation, preprint Version 1 arXiv:1904.10207v1, later split into:
CMP 377(3) 2020 (not containing discussion of M5-brane anomalies)
SS 20 (focusing on the M5-brane anomaly cancellation)
and then expanding out the paragraph on the previously omitted term as follows:
This basic form component $G_4^{M5}$ (6) had been ignored in FHMM 98 and previous references. That this basic form component $G_4^{M5}$ (6) indeed needs to be considered was pointed out in FSS 19v1, (19), BBMN 19b, (3.16) & App. C (where it is denoted $\gamma_4$, see also BBM 20 (2.3)) and SS 20, (3) & p. 5.
added pointer to today’s:
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