Thermodynamics of the Complex su(3) Toda Theory

Abstract

We present the first computation of the thermodynamic properties of the complex su(3) Toda theory. This is possible thanks to a new string hypothesis, which involves bound states that are non self-conjugate solutions of the Bethe equations. Our method provides equivalently the solution of the su(3) generalization of the XXZ chain. In the repulsive regime, we confirm that the scattering theory proposed over the past few years - made only of solitons with non diagonal S-matrices - is complete. But we show that unitarity does not follow, contrary to early claims, eigenvalues of the monodromy matrix not being pure phases. In the attractive regime, we find that the proposed minimal solution of the bootstrap equations is actually far from being complete. We discuss some simple values of the couplings, where, instead of the few conjectured breathers, a very complex structure (involving E_6, or two E_8) of bound states is necessary to close the bootstrap.

6 pages, 2 figures; some minor changes; accepted for publication in Phys. Lett. B

References in corpus (7)

• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
• gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions
• The Exact S-Matrix for an osp(2|2) Disordered System
• Self-duality in quantum impurity problems
• Non-unitarity in quantum affine Toda theory and perturbed conformal field theory
• Soliton S matrices for the critical A_{N-1}^(1) chain

Cited by in corpus (16)

• Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• Integrability of the AdS_5 x S^5 superstring and its deformations
• The Quantum Deformed Mirror TBA I
• Introduction to the thermodynamic Bethe ansatz
• Integrable quantum field theories with OSP(m/2n) symmetries
• Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure
• Integrable aspects of the scaling q-state Potts models II: finite-size effects
• The continuum limit of $a_{N-1}^{(2)}$ spin chains
• RSOS revisited
• Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• Continuum Limit of gl(M/N) Spin Chains
• Fusion hierarchies, $T$-systems and $Y$-systems for the $A_2^{(1)}$ models
• Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras
• A diagrammatic approach towards the thermodynamics of integrable systems