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Abstract
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We obtain (2+1)-dimensional gravity with cosmological constant which is coupled to gauge fields,
using Maxwell and semisimple extension of the Poincaré gauge symmetric models (i.e., Chern-Simons
models with these gauge groups). Also, we obtain some AdS-and BTZ-type solutions for the classical
equations of motion for these (2 þ 1)-dimensional gravities. For the semisimple extension of the Poincaré
gauge group we investigate the AdS/CFT correspondence and show that the model at the boundary is
equivalent to the sum of three Wess-Zumino-Witten models over group SOð2; 1Þ. Then, we show that the
central charge of the CFT is the same as that of CFTat the boundary of AdS spacetime related to the Chern-
Simons model with gauge group SOð2; 2Þ. Finally, we show that these two (2 þ 1)-dimensional gravity
models are dual (canonically transformed) to each other.
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