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We present and study a 4d Chern-Simons (CS) model whose gauge symmetry isencoded in a balanced Lie group crossed module. Using the derived formal set-uprecently found, the model can be formulated in a way that in many respectsclosely parallels that of the familiar 3d CS one. In spite of these formalresemblance, the gauge invariance properties of the 4d CS model differconsiderably. The 4d CS action is fully gauge invariant if the underlying base4fold has no boundary. When it does, the action is gauge variant, the gaugevariation being a boundary term. If certain boundary conditions are imposed onthe gauge fields and gauge transformations, level quantization can then occur.In the canonical formulation of the theory, it is found that, depending againon boundary conditions, the 4d CS model is characterized by surface chargesobeying a non trivial Poisson bracket algebra. This is a higher counterpart ofthe familiar WZNW current algebra arising in the 3d model. 4d CS theory thusexhibits rich holographic properties. The covariant Schroedinger quantizationof the 4d CS model is performed. A preliminary analysis of 4d CS edge fieldtheory is also provided. The toric and Abelian projected models are describedin some detail.

4-d Chern-Simons Theory: Higher Gauge Symmetry and Holographic Aspects