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adding references on the suggestion that an actual E8-principal bundle on 11d spacetime plays a role here:
D. Diaconescu, Gregory Moore, Edward Witten, E8 Gauge Theory, and a Derivation of K-Theory from M-Theory, Adv. Theor. Math. Phys. 6:1031-1134, 2003 (arXiv:hep-th/0005090)
E. Diaconescu, Dan Freed, Greg Moore, Section 3 in: The M-theory 3-form and E8-gauge theory, chapter in Haynes Miller, Douglas Ravenel (eds.) Elliptic Cohomology Geometry, Applications, and Higher Chromatic Analogues, Cambridge University Press 2007 (arXiv:hep-th/0312069, doi:10.1017/CBO9780511721489)
Allan Adams1, Jarah Evslin, The loop group of E8 and K-theory from 11d, JHEP 02 (2003) (arXiv:hep-th/0203218)
Hisham Sati, E8 Gauge Theory and Gerbes in String Theory, Adv. Theor. Math. Phys. 14:1-39, 2010 (arXiv:hep-th/0608190)
added pointer to:
Andres Collinucci, Raffaele Savelli, On Flux Quantization in F-Theory, J. High Energ. Phys. 2012 15 (2012) [arXiv:1011.6388, doi:10.1007/JHEP02(2012)015]
Andres Collinucci, Raffaele Savelli, On Flux Quantization in F-Theory II: Unitary and Symplectic Gauge Groups, J. High Energ. Phys. 2012 94 (2012) [arXiv:1203.4542, doi:10.1007/JHEP08(2012)094]
added pointer to today’s proof that C-field flux quantization in stable Cohomotopy implies the desired divisibility by 6 of the D=11 supergravity action functional:
This is really cool. It’s nice to see that E_8 isn’t needed here, which always seemed slightly ad-hoc (even though the yoga of exceptionalism would suggest it’s ok to have that group turn up).
The vanishing of the unstable version (as far as I understood it) in the last theorem was surprising, can you say what that “means”? The headline fact, integrality of 1/6th of the obvious cubic action, is reasonable, but then surely one expects from the whole 4-cohomotopy game that the unstable version is the ’real’ thing? Please enlighten me!
In order to know what the result means in the context that it is presented, one will first have to decide what meaning to attach to the value of the action functional on a given field history. Usually people say this is needed for the path integral, which of course is misleading, but that’s where the interest in these expressions traditionally comes from.
The way I look at 11d SuGra (here) the Lagrangian density and hence these questions never come up. But elsewhere it’s regarded as a big deal and then it seems noteworthy to know that there are these results concerning Cohomotopy.
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