Generalized KdV and Quantum Inverse Scattering Description of Conformal Minimal Models

Abstract

We propose an alternative description of 2 dimensional Conformal Field Theory in terms of Quantum Inverse Scattering. It is based on the generalized KdV systems attached to $A_2^{(2)}$, yielding the classical limit of Virasoro as Poisson bracket structure. The corresponding T-system is shown to coincide with the one recently proposed by Kuniba and Suzuki. We classify the primary operators of the minimal models that commute with all the Integrals of Motion, and that are therefore candidates to perturb the model by keeping the conservation laws. For our $A_2^{(2)}$ structure these happen to be ${\varphi }_{1,2},{\varphi }_{2,1},{\varphi }_{1,5}$, in contrast to the $A_1^{(1)}$ case, studied by Bazhanov, Lukyanov and Zamolodchikov~\cite{BLZ}, related to ${\varphi }_{1,3}$.

12 pages, latex. 1 reference added

References in corpus (3)

• Functional Relations and Analytic Bethe Ansatz for Twisted Quantum Affine Algebras
• New functional dilogarithm identities and sine-Gordon Y-systems
• Integrable Perturbations of $W_n$ and WZW Models

Cited by in corpus (21)

• Integrable Quantum Field Theories in Finite Volume: Excited State Energies
• Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• Superconformal Field Theory and SUSY N=1 KdV Hierarchy II: The Q-operator
• Exact conserved quantities on the cylinder I: conformal case
• Superconformal Field Theory and SUSY N=1 KdV Hierarchy I: Vertex Operators and Yang-Baxter Equation
• Integrable Structure of Superconformal Field Theory and Quantum super-KdV Theory
• The perturbations ${\varphi }_{2,1}$ and ${\varphi }_{1,5}$ of the minimal models $M(p,p^{\prime })$ and the trinomial analogue of Bailey's lemma
• Affine Yangian of $\mathfrak{gl}(2)$ and integrable structures of superconformal field theory
• Integrable aspects of the scaling q-state Potts models II: finite-size effects
• Spectrum of the reflection operators in different integrable structures
• Integrals of motion from TBA and lattice-conformal dictionary
• Generalized q-Onsager Algebras and Dynamical K-matrices
• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
• Integrable structure of $\text{BCD}$ conformal field theory and boundary Bethe ansatz for affine Yangian
• Thermodynamic Bethe Ansatz for the subleading magnetic perturbation of the tricritical Ising model
• Excited State TBA for the ${\varphi }_{2,1}$ perturbed $M_{3,5}$ model
• Central Charge and the Andrews-Bailey Construction
• An inhomogeneous Lax representation for the Hirota equation
• Quantum Inverse Scattering Method and (Super)Conformal Field Theory
• Three realizations of quantum affine algebra $U_q(A_2^{(2)})$
• The ODE/IM Correspondence between $C(2{)}^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT