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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics