TBA equations for excited states in the Sine-Gordon model

Abstract

We propose TBA integral equations for multiparticle soliton (fermion) states in the Sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe Ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-deVega equation) description of the model is given.

arXiv comment30 pages, latex, minor changes

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
• Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories
• Excited states by analytic continuation of TBA equations
• Integrable Quantum Field Theories in Finite Volume: Excited State Energies
• Excited State Destri - De Vega Equation for Sine-Gordon and Restricted Sine-Gordon Models
• Dynkin TBA's
• 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
• Excited states in some simple perturbed conformal field theories
• Continued fraction TBA and functional relations in XXZ model at root of unity
• Scaling Functions in the Odd Charge Sector of Sine-Gordon/Massive Thirring Theory
• From Fusion Hierarchy to Excited State TBA
• Excited-state thermodynamics
• Sigma models as perturbed conformal field theories
• Non-Linear Integral Equations for complex Affine Toda associated to simply laced Lie algebras
• Nonlinear Integral Equation and Finite Volume Spectrum of Minimal Models Perturbed by ${\Phi }_{(1,3)}$
• Excited TBA Equations I: Massive Tricritical Ising Model
• New functional dilogarithm identities and sine-Gordon Y-systems
• Excited TBA Equations II: Massless Flow from Tricritical to Critical Ising Model
• Excited State TBA for the ${\varphi }_{2,1}$ perturbed $M_{3,5}$ model

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