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

Understand

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.