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We derive a local, gauge invariant action for the SU(N) non-linearsigma-model in 2+1 dimensions. In this setting, the model is defined in termsof a self-interacting pseudo vector-field \theta_\mu, with values in the Liealgebra of the group SU(N). Thanks to a non-trivially realized gaugeinvariance, the model has the correct number of degrees of freedom: only onepolarization of \theta_\mu, like in the case of the familiar Yang-Mills theoryin 2+1 dimensions. Moreover, since \theta_\mu is a pseudo-vector, the physicalcontent corresponds to one massless pseudo-scalar field in the Lie algebra ofSU(N), as in the standard representation of the model. We show that thedynamics of the physical polarization corresponds to that of the SU(N)non-linear sigma model in the standard representation, and also construct thecorresponding BRST invariant gauge-fixed action.Comment: LaTeX, 15 pages, no figure

A gauge-invariant formulation for theSU(N) nonlinear -model in 2 1 dimensions