Schreiber ∞-Wess-Zumino-Witten theory

An article that we are preparing

• Domenico Fiorenza, Hisham Sati, Urs Schreiber,

  $\infty$-Wess-Zumino-Witten theory

on higher analogs of the WZW model and their holographic relation to ∞-Chern-Simons theory.

See

• Domenico Fiorenza, Hisham Sati, Urs Schreiber,

  Super Lie n-algebra extensions, higher WZW models and super p-branes with tensor multiplet fields

Exposition of this is in the following talk notes

• Urs Schreiber,

  WZW terms in a cohesive $\infty$-topos ,

  talk at Representation Theoretic and Categorical Structures in Quantum Geometry and Conformal Field Theory (2011)

  (pdf slides)

• Urs Schreiber

  Higher geometric prequantum theory and The brane bouquet

  talk at Bayrischzell workshop 2013

  (pdf notes)

Idea

In the context of differential cohomology in a cohesive topos, every characteristic map $\mathbf{c}$ induces – via ∞-Chern-Weil theory – the Lagrangian $CS_{\mathbf{c}}$ of an ∞-Chern-Simons theory. There is canonically a differentially twisted looking $WZW_{\mathbf{c}}$ of $CS_{\mathbf{c}}$. This generalizes the Lagrangian for the sigma-model called the Wess-Zumino-Witten model from Lie group target spaces to general smooth ∞-group target spaces.

Related projects

• differential cohomology in a cohesive topos

  • Synthetic Quantum Field Theory

    • Quantum gauge field theory in Cohesive homotopy type theory

    • Type-semantics for quantization

  • cohomology

    • Principal ∞-bundles – theory, presentations and applications

    • Fivebrane structures

  • ∞-Chern-Weil theory

    • L-∞ algebra connections

    • Cech cocycles for differential characteristic classes

    • Twisted differential structures

      • Twisted Differential String and Fivebrane Structures

      • The moduli 3-stack of the C-field

  • ∞-Chern-Simons theory

    • Higher Chern-Weil Derivation of AKSZ Sigma-Models

    • nonabelian 7d Chern-Simons theory and the 5-brane

    • Extended higher cup-product Chern-Simons theories

  • ∞-Wess-Zumino-Witten theory

    • The brane bouquet

    • Obstruction theory for parameterized higher WZW terms

  • Higher geometric prequantum theory

    • Classical field theory via higher differential geometry

    • Local prequantum field theory

    • L-∞ algebras of local observables from higher prequantum bundles

    • Higher extensions of mapping class groups

  • Motivic quantization of local prequantum field theory

    • Geometric quantization of symplectic and Poisson manifolds

    • Cohomological quantization of local prequantum boundary field theory