The curious case of large-N expansions on a (pseudo)sphere
High Energy Physics - Theory
2015-02-11 v2 Strongly Correlated Electrons
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1412.1437,
title = {The curious case of large-N expansions on a (pseudo)sphere},
author = {Alexander M. Polyakov and Zain H. Saleem and James Stokes},
journal= {arXiv preprint arXiv:1412.1437},
year = {2015}
}
Comments
18 pages, 3 figures