Schreiber
Synthetic prequantum field theory in a cohesive homotopy topos
Contents
on differential cohomology in a cohesive homotopy topos and Higher Prequantum Geometry.
Contents
Motivation
Prequantum geometry
| 20th century | particle physics | brane physics | 21st century |
|---|
| manifolds | spacetime, phase space | higher super-orbifolds | supergeometric étale ∞-stack |
| fiber bundles with connection | gauge field magnetic charges, prequantum line bundles | brane charges in twisted equivariant differential generalized cohomology (e.g. F1/Dp-brane charges in twisted differential real K-theory on orientifolds) | cohesive sheaves of parameterized spectra |
| Cartan geometry | gravity | higher dimensional supergravity | higher super Cartan geometry |
| Chern-Weil theory | instantons, Chern-Simons theory, WZW terms | Prequantum field theories from Shifted symplectic structures (AKSZ sigma-models such as PSM, A-model, B-model, CSM, also 7d CS theory, 11d CS theory, string field theory) | infinity-Chern-Simons theory, infinity WZW theory |
| open problems: | | | lift F1/Dp-brane charges to M2/M5-brane charges in something like ADE-equivariant stable differential cohomotopy | unfeasible in compontents – need synthetic theory: homotopy toposes with progression of adjoint modal operators: “super differential cohesive homotopy toposes” |
| | | this I will discuss in the next two weeks at ESI Vienna, in a lecture series “Prequantum field theory and the Green-Schwarz WZW terms” and in a contributed talk “Generalized cohomology of M2/M5-branes” | this I am surveying today, from “differential cohomology in a cohesive homotopy topos” |
Details
The talk follows the notes at super Cartan geometry.
Exposition and survey is at Higher Prequantum Geometry.
A fairly comprehensive account is at differential cohomology in a cohesive homotopy topos.
Last revised on December 21, 2015 at 13:04:51.
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