Non-Lagrangian construction of abelian CS/FQH-theory via flux quantization in 2-Cohomotopy

Abstract: After briefly recalling how the analog of Dirac charge quantization in exotic (effective, higher) gauge theories, providing their global topological completion, is encoded in a choice of classifying space $𝒜$ whose rationalization reflects the flux Bianchi identities, I explain how the choice $𝒜 ≔ S^2$ (“flux quantization in 2-Cohomotopy”) implements effective corrections to ordinary Dirac flux quantization, which over surfaces yields exactly the topological quantum observables of fractional quantum Hall systems, traditionally described by abelian Chern-Simons theory. I close by briefly indicating how this situation is geometrically engineered on probe M5-branes if the M-theory C-field is flux-quantized in 4-Cohomotopy (“Hypothesis H”). This is joint work with Hisham Sati; for more pointers see ncatlab.org/schreiber/show/ISQS25.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

( slides )

Topology and Geometry Seminar (Texas, Kansas)