4-d semistrict higher Chern-Simons theory I

Understand

We formulate a 4-dimensional higher gauge theoretic Chern-Simons theory.

• Its symmetry is encoded in a semistrict Lie 2-algebra equipped with an invariant non singular bilinear form.
• We analyze the gauge invariance of the theory and show that action is invariant under a higher gauge transformation up to a higher winding number.
• We find that the theory admits two seemingly inequivalent canonical quantizations.