Séminaire Physique mathématique ICJ

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

## by Prof. Roberto Zucchini

Europe/Paris
Zoom (Institut Camille Jordan)

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#### Institut Camille Jordan

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Description
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. 
Organized by

Nguyen-Viet Dang

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