Séminaire Physique mathématique ICJ

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

by Prof. Roberto Zucchini

Zoom (Institut Camille Jordan)


Institut Camille Jordan

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We present and study a 4--d Chern--Simons (CS) model whose gauge symmetry
is encoded in a balanced Lie group crossed module.  Using the derived formal set--up, 
the model can be formulated in a way that in many respects closely parallels that of the 
familiar 3--d CS one. In spite of these formal resemblance, the gauge invariance properties
of the 4--d CS model differ considerably. The 4–d CS action is fully gauge invariant if the 
underlying base 4–fold has no boundary. When it does, the action is gauge variant, the gauge 
variation being a boundary term. If certain boundary conditions are imposed on the gauge fields 
and gauge transformations, level quantization can then occur. In the canonical formulation of the 
theory, it is found that, depending again on boundary conditions, the 4--d CS model is characterized 
by surface charges obeying a non trivial Poisson bracket algebra. This is a higher counterpart of 
the familiar WZNW current algebra arising in the 3–d model. 4--d CS theory thus exhibits rich 
holographic properties. 
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Nguyen-Viet Dang