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
WZW terms in a cohesive $\infty$-topos ,
talk at Representation Theoretic and Categorical Structures in Quantum Geometry and Conformal Field Theory (2011)
Higher geometric prequantum theory and The brane bouquet
talk at Bayrischzell workshop 2013
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.
differential cohomology in a cohesive topos
∞-Wess-Zumino-Witten theory