Spectrum of the reflection operators in different integrable structures

Abstract

The reflection operators are the simplest examples of the non-local integrals of motion, which appear in many interesting problems in integrable CFT. For the so-called Fateev, quantum AKNS, paperclip and KdV integrable structures, they are built from the (chiral) reflection S-matrices for the Liouville and cigar CFTs. Here we give the full spectrum of the reflection operators associated with these integrable structures. We also obtained a relation between the reflection S-matrices of the cigar and Liouville CFTs. The results of this work are applicable for the description of the scaling behaviour of the Bethe states in exactly solvable lattice systems and may be of interest to the study of the Generalized Gibbs Ensemble associated with the above mentioned integrable structures.

33 pages, published version

References in corpus (17)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• 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 W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• Beyond the Large N Limit: Non-linear W(infinity) as symmetry of the SL(2,R)/U(1) coset model
• Baxter's Q-operators for supersymmetric spin chains
• Integrable Model of Boundary Interaction: The Paperclip
• Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
• Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
• Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states
• Generalized KdV and Quantum Inverse Scattering Description of Conformal Minimal Models
• Exact generalized partition function of 2D CFTs at large central charge
• The ^sl(2)+^sl(2)/^sl(2) Coset Theory as a Hamiltonian Reduction of ^D(2|1;α)
• Quantum transfer-matrices for the sausage model
• On the scaling behaviour of the alternating spin chain
• Integrable boundary interaction in 3D target space: the "pillow-brane" model
• Bethe state norms for the Heisenberg spin chain in the scaling limit

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• Scaling limit of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ invariant boundary conditions
• ODE/IQFT correspondence for the generalized affine $\mathfrak{sl}(2)$ Gaudin model