Synthetic prequantum field theory in a cohesive homotopy topos


on differential cohomology in a cohesive homotopy topos and Higher Prequantum Geometry.



Prequantum geometry

20th centuryparticle physicsbrane physics21st century
manifoldsspacetime, phase spacehigher super-orbifoldssupergeometric étale ∞-stack
fiber bundles with connectiongauge field magnetic charges, prequantum line bundlesbrane 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 geometrygravityhigher dimensional supergravityhigher super Cartan geometry
Chern-Weil theoryinstantons, Chern-Simons theory, WZW termsPrequantum 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 cohomotopyunfeasible 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-branesthis I am surveying today, from “differential cohomology in a cohesive homotopy topos


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 08:04:51. See the history of this page for a list of all contributions to it.