Schreiber
∞-Wess-Zumino-Witten theory

An article that we are preparing

• Domenico Fiorenza, Hisham Sati, Urs Schreiber,

  $\mathrm{\infty }$-Wess-Zumino-Witten theory

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

For the moment, an exposition of some aspects can be found in

• Urs Schreiber,

  WZW terms in a cohesive $\mathrm{\infty }$-topos ,

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

  (pdf slides)

Idea

In the context of differential cohomology in a cohesive topos, every characteristic map $c$ induces – via ∞-Chern-Weil theory – the Lagrangian ${\mathrm{CS}}_c$ of an ∞-Chern-Simons theory. There is canonically a differentially twisted looking ${\mathrm{WZW}}_c$ of ${\mathrm{CS}}_c$. 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

  • Quantum gauge field theory in Cohesive homotopy type theory

  • 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

  • Higher geometric prequantum theory

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