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I would like to ask if it is possible to regard the Polyakov action as an effective action that describes the broken symmetric phase of a more general model. Could someone draw an analogy with O(N) Non-linear sigma model that describes the broken symmetric phase of a O(N) phi^4? What would be that model in the stringy case?

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I believe that as in the O(3) case we relax the nonlinear constraint and can ''move'' in a normal direction to the sphere, the same could happen in the general Nlsm, and we correspondingly have the emergence of ''normal move'' from the metric, so i suppose the new model that we could take will require a bigger target space... –  Panagiotis Betzios May 6 '12 at 13:45

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