In the physics-minded string theory community, parts of the literature tends to forget or downplay the conjectural nature of many assumptions and leaps of faiths that are being made when it comes to discussion of D-brane/ M-brane dynamics and generally of non-perturbative effects in string theory. It is an open problem to mathematically formulate M-theory: Supposedly a single coherent theory of physics whose various limiting cases reproduce the zoo of perturbative string theories ( HET/ I/ IIA/ IIB& F/ 11d SuGra) and the expected dualities relating them but which also makes mathematical sense of non-perturbative D-/ M-brane physics, and hence solves, via intersecting D-brane models of confined quantum Yang-Mills theory ( holographic QCD), the last of the Millennium Problems: (In a play on how the “M” in “M-theory” has been said to be either for “Membrane” or for “Mystery”, so the “H” in “Hypothesis H” may be read as being either for “Homotopy” or for “Hisham”.) 2.5) and has become the theme of a research program developed by Hisham Sati and Urs Schreiber, see the list of references below.
This originates with an observation due to Sati 2013 ( Sec. The core statement of the hypothesis is that quantum charge quantization in M-theory happens in the non-abelian cohomology theory called Cohomotopy (in more detail: twisted Cohomotopy). Hypothesis H is a hypothesis about the mathematical formulation of the theory of fundamental physics known as M-theory.
Motivation from homotopy theoretic re-analysis of the brane-scan.The open problem of formulating M-Theory.
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