#
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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