The matrix Chern-Simons one-form as a Universal Chern-Simons theory

We consider different large N limits of the one-dimensional Chem-Simons action i integral dt Tr(partial derivative(0) + A(0)) where A(0) is an N x N anti-Hermitian matrix. The Hilbert space on which A(0) acts as a linear transformation is taken as the quantization of a 2k-dimensional phase space M with different gauge field backgrounds. For slowly varying fields, the large N limit of the one-dimensional CS action is equal to the (2k + I)dimensional CS theory on M x R. Different large M limits are parametrized by the gauge fields and the dimension 2k. The result is related to the bulk action for quantum Hall droplets in higher dimensions. Since the isometries of M are gauged, this has implications for gravity on fuzzy spaces. This is also briefly discussed. (c) 2006 Elsevier B.V. All fights reserved.