On the Derivation of Twisted K-Theory from M-Theory

Abstract: In a restricted untwisted sector, Diaconescu, Moore & Witten (2000, 2003) gave a quantum M-theoretic consistency check, at the level of partition functions, of what one may call "Hypothesis K", namely that magnetic and electric type IIA brane charges are jointly quantized in K-theory. We show that the more recently discussed "Hypothesis H" --- that magnetic and electric charges in 11D are jointly quantized in coHomotopy --- together with a topological smallness condition on the M-theory circle, systematically implies that IIA charges are quantized in a nonabelian deformation of twisted K-theory by the previously neglected non-linear NS1-brane charge. This is essentially a derivation of twisted K-theory from IR-completed 11D SuGra, and conversely a further consistency check on Hypothesis H from Hypothesis K. We motivate and precisely state this result, discuss its structural implications, and outline the elaborate algebro-topological proof.