TBA equations for the mass gap in the non-linear σ-models

2005/04/22 by János Balog, J. Balog, A. Hegedus +1 · 19 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Basis (linear algebra) #Cold Atom Physics and Bose-Einstein Condensates #Differential equation #Geometry #Independent equation #Mass gap #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Sigma #Sigma model #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2005.07.032

published in Nuclear Physics B 725(3), 531-553 (Elsevier BV) · 24 pages, LaTeX

arxiv created 2005/04/22 · openalex publication_date 2005/08/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We propose TBA integral equations for 1-particle states in the O(n) non-linear sigma-model for even n. The equations are conjectured on the basis of the analytic properties of the large volume asymptotics of the problem, which is explicitly constructed starting from Luscher's asymptotic formula. For small volumes the mass gap values computed numerically from the TBA equations agree very well with results of three-loop perturbation theory calculations, providing support for the validity of the proposed TBA system.

Citations

• A determination of the mass gap in the 0(n) σ-model
• Dynkin TBA's
• TBA equations for excited states in theO(3) andO(4) nonlinear -model
• Excited TBA equations II: massless flow from tricritical to critical Ising model
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• TBA equations for excited states in the sine–Gordon model
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models