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We elucidate the large-N dynamics of one-dimensional sigma models withspherical and hyperbolic target spaces and find a duality between the Lagrangemultiplier and the angular momentum. In the hyperbolic model we propose a newclass of operators based on the irreducible representations of hyperbolicspace. We also uncover unexpected zero modes which lead to the double scalingof the 1/N expansion and explore these modes using Gelfand-Dikiy equations.

The curious case of large-N expansions on a (pseudo)sphere