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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, 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 -theory 3-form and -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 and K-theory from 11d, JHEP 02 (2003) (arXiv:hep-th/0203218)
Hisham Sati, 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]
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