Geometric and topological structures related to M-branes
Hisham Sati
TL;DR
The work integrates M-theory's C-field and its dual with String and Fivebrane structures, framing their quantization and dualities through higher cohomology theories. It develops a dual, twist-aware language using $L_\infty$-algebras and differential characters to describe gauge data, and proposes TMF (twisted Topological Modular Forms) as the natural home for M-brane charges, paralleling twisted K-theory for D-branes. By exploring dualities, higher differential characters, mapping spaces, and determinantal gerbes, the paper argues that TMF twists organize M-theory topological data and give a principled way to define anomaly-free partition functions for M2- and M5-branes. This framework suggests deep connections between M-theory, elliptic cohomology, and higher categorical structures, with potential implications for charge quantization, dualities, and nonperturbative dynamics.
Abstract
We consider the topological and geometric structures associated with cohomological and homological objects in M-theory. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying spacetime to admit a String structure and a Fivebrane structure, respectively. For the former, we study how the fields in M-theory are associated with the above structures, with homotopy algebras, with twisted cohomology, and with generalized cohomology. We also explain how the corresponding charges should take values in Topological Modular forms. We survey background material and related results in the process.