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

We consider different large NN limits of the one-dimensional Chern–Simons action i∫dtTr(∂0+A0)i∫dtTr(∂0+A0) where A0A0 is an N×NN×N anti-Hermitian matrix. The Hilbert space on which A0A0 acts as a linear transformation is taken as the quantization of a 2k  -dimensional phase space MM with different gauge field backgrounds. For slowly varying fields, the large NN limit of the one-dimensional CS action is equal to the (2k+1)(2k+1)-dimensional CS theory on M×RM×R. Different large NN 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 MM are gauged, this has implications for gravity on fuzzy spaces. This is also briefly discussed.