Semistrict analogues of the five-dimensional strict HCS theory

Determine whether the five-dimensional higher Chern–Simons theory constructed in the strict setting has higher-dimensional analogues within the semistrict homotopy-theoretic framework based on balanced 2-term $L_\infty$-algebras.

Background

The paper generalizes four-dimensional semistrict higher Chern–Simons theory to even dimensions $2n+2$ for balanced 2-term $L_\infty$-algebras and recovers previously known strict theories as special cases. It leaves unresolved whether the strict five-dimensional HCS construction of Song et al. can be embedded in, or extended through, the semistrict homotopy-theoretic framework developed here.

Addressing this question would clarify the scope of semistrict higher Chern–Simons constructions and establish whether higher-dimensional counterparts of the strict five-dimensional model exist when the trilinear bracket and other semistrict structures are present.