An eigenvalue problem related to the non-linear sigma-model: analytical and numerical results

Abstract

An eigenvalue problem relevant for non-linear sigma model with singular metric is considered. We prove the existence of a non-degenerate pure point spectrum for all finite values of the size R of the system. In the infrared (IR) regime (large R) the eigenvalues admit a power series expansion around IR critical point R\to\infty. We compute high order coefficients and prove that the series converges for all finite values of R. In the ultraviolet (UV) limit the spectrum condenses into a continuum spectrum with a set of residual bound states. The spectrum agrees nicely with the central charge computed by the Thermodynamic Bethe Ansatz method

18 pages, AmsLatex, Axodraw

References in corpus (1)

• Geometrical interpretation of D-branes in gauged WZW models

Cited by in corpus (5)

• The ODE/IM Correspondence
• A Gradient Flow for Worldsheet Nonlinear Sigma Models
• On sigma model RG flow, "central charge" action and Perelman's entropy
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
• Integrable Deformations of Sine-Liouville Conformal Field Theory and Duality