Nonlinear integral equations for finite volume excited state energies of the O(3) and O(4) nonlinear sigma-models

Abstract

We propose nonlinear integral equations for the finite volume one-particle energies in the O(3) and O(4) nonlinear sigma-models. The equations are written in terms of a finite number of components and are therefore easier to solve numerically than the infinite component excited state TBA equations proposed earlier. Results of numerical calculations based on the nonlinear integral equations and the excited state TBA equations agree within numerical precision.

arXiv commentnumerical results added

References in corpus (23)

• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Excited states by analytic continuation of TBA equations
• Integrable Quantum Field Theories in Finite Volume: Excited State Energies
• Non linear integral equation and excited--states scaling functions in the sine-Gordon model
• Nonlinear Integral Equation and Finite Volume Spectrum of Sine-Gordon Theory
• Truncated Conformal Space at c=1, Nonlinear Integral Equation and Quantization Rules for Multi-Soliton States
• Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures
• Excited states in some simple perturbed conformal field theories
• Excited-state thermodynamics
• TBA equations for excited states in the O(3) and O(4) nonlinear $\sigma$-model
• Sigma models as perturbed conformal field theories
• Correction to four-loop RG functions in the two-dimensional lattice O(n) $\sigma$-model
• Finite size effects and the supersymmetric sine-Gordon models
• Nonstandard Cutoff Effects in the Nonlinear Sigma Model
• Excited TBA Equations I: Massive Tricritical Ising Model
• TBA equations for excited states in the Sine-Gordon model
• Excited states nonlinear integral equations for an integrable anisotropic spin 1 chain
• Excited TBA Equations II: Massless Flow from Tricritical to Critical Ising Model
• A determination of the mass gap in the O(n) sigma model
• Finite size effects in the SS-model: two component nonlinear integral equations
• Excited State TBA for the ${\varphi }_{2,1}$ perturbed $M_{3,5}$ model

Cited by in corpus (12)

• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• String hypothesis for the AdS_5 x S^5 mirror
• Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics
• Konishi operator at intermediate coupling
• Temperature quantization from the TBA equations
• $Ad{S}_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations
• Hybrid-NLIE for the AdS/CFT spectral problem
• Finite Size Spectrum of SU(N) Principal Chiral Field from Discrete Hirota Dynamics
• The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model
• Finite size effects and 2-string deviations in the spin-1 XXZ chains
• Contour deformation trick in hybrid NLIE
• A numerical test of the Y-system in the small size limit of the SU(2)x SU(2) Principal Chiral Model