An article that we have written:
Domenico Fiorenza, Hisham Sati, Urs Schreiber,
Twisted Cohomotopy implies M-Theory anomaly cancellation on 8-manifolds
Communications in Mathematical Physics
377 (2020) 1961-2025
download file:
concise survey: pdf
Abstract. We show that all the expected anomaly cancellations in M-theory follow from charge-quantizing the C-field in the non-abelian cohomology theory twisted Cohomotopy (“Hypothesis H”). Specifically, we show that such cocycles exhibit all of the following:
Along the way, we find that the calibrated $N =1$ exceptional geometries (${Spin}(7)$, $G_2$, ${SU}(3)$, ${SU}(2)$) are all induced from the classification of twists in Cohomotopy. Finally we show that the notable factor of $1/24$ in the anomaly polynomial reflects the order of the 3rd stable homotopy group of spheres.
Based on:
Domenico Fiorenza, Hisham Sati, Urs Schreiber:
The rational higher structure of M-theory,
Proceedings of the LMS-EPSRC Durham Symposium:
Higher Structures in M-Theory 2018
Fortschritte der Physik, 2019
Followups (Hypothesis H):
Domenico Fiorenza, Hisham Sati, Urs Schreiber:
Domenico Fiorenza, Hisham Sati, Urs Schreiber:
Equivariant Cohomotopy implies orientifold tadpole cancellation
Lift of fractional D-brane charge to equivariant Cohomotopy theory
Differential Cohomotopy implies intersecting brane observables
Domenico Fiorenza, Hisham Sati, Urs Schreiber:
Twisted Cohomotopy implies twisted String structure on M5-branes
Domenico Fiorenza, Hisham Sati, Urs Schreiber:
Twistorial Cohomotopy implies Green-Schwarz anomaly cancellation
Talk notes:
talk at Souriau 2019
IHP Paris, May 2019
Related talks:
Super p-Brane Theory emerging from Super Homotopy Theory
talk at StringMath2017,
Hamburg 2017
Equivariant Cohomotopy and Branes
talk at String and M-Theory: The New Geometry of the 21st Century,
Singapore 2018
The rational higher structure of M-theory
talk at Higher Structures in M-Theory,
Durham 2018
Last revised on October 31, 2021 at 12:51:41. See the history of this page for a list of all contributions to it.