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arXiv · 1412.1437

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

Alexander M. Polyakov·Zain H. Saleem·James Stokes
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Abstract

We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of operators based on the irreducible representations of hyperbolic space. We also uncover unexpected zero modes which lead to the double scaling of the 1/N expansion and explore these modes using Gelfand-Dikiy equations.

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Alexander M. Polyakov, Zain H. Saleem, James Stokes. 2015-02-10. The curious case of large-N expansions on a (pseudo)sphere. https://doi.org/10.1016/j.nuclphysb.2015.01.024

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