Integrability of a family of quantum field theories related to sigma models

DOI10.1016/j.nuclphysb.2011.07.019zbMath1229.81207arXiv1102.5716OpenAlexW2147745433MaRDI QIDQ659330

Jörg Teschner, David Ridout

Publication date: 18 January 2012

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.5716

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Supersymmetric field theories in quantum mechanics (81T60) Quantum field theory on lattices (81T25) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse scattering problems in quantum theory (81U40) Groups and algebras in quantum theory and relations with integrable systems (81R12) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items (11)

Lambda models from Chern-Simons theories ⋮ Asymptotic representations and \(q\)-oscillator solutions of the graded Yang-Baxter equation related to Baxter Q-operators ⋮ Infinite-dimensional R-matrices for the relativistic scattering of massless modes on \(\mathrm{AdS}_2\) ⋮ A study of integrable form factors in massless relativistic \(AdS_2\) ⋮ Integrable sigma models at RG fixed points: quantisation as affine Gaudin models ⋮ On $\boldsymbol {AdS_2/CFT_1}$ transfer matrices, Bethe ansatz and scale invariance ⋮ Massless \(\mathrm{AdS}_{2}\) scattering and Bethe ansatz ⋮ Baxter operators and Hamiltonians for ``nearly all integrable closed \(gl(n\)) spin chains ⋮ Integrable lambda models and Chern-Simons theories ⋮ Free fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT ⋮ Geometry of massless scattering in integrable superstring

Cites Work

• Unnamed Item
• Review of AdS/CFT integrability, chapter VI.1: Superconformal symmetry
• Integrable structure of superconformal field theory and quantum super-KdV theory
• Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras
• \(N=2\) super KdV and super sine-Gordon equations based on Lie super algebra \(A(1,1)^{(1)}\).
• Superconformal field theory and SUSY \(N=1\) KdV hierarchy. II: the \(Q\)-operator
• Quantum group structure in the Fock space resolutions of ŝl(n) representations
• Quantum inverse problem method. I
• On the spectrum of the sinh-Gordon model in finite volume
• Pohlmeyer reduction of \(\text{AdS}_5\times S^5\) superstring sigma model
• Baxter's Q-operators for supersymmetric spin chains
• Quantization of the \(N=2\) supersymmetric KdV hierarchy
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Lie superalgebraic approach to super Toda lattice and generalized super KdV equations
• Quantum group symmetries and non-local currents in 2D QFT
• The uniqueness theorem for the universal \(R\)-matrix
• Integrable structure of conformal field theory. III: The Yang-Baxter relation
• Quantized enveloping algebras associated with simple Lie superalgebras and their universal \(R\)-matrices
• Hirota equation as an example of an integrable symplectic map
• Quantum lattice KdV equation
• Yang-Baxterization of quantum dilogarithm
• Quantum discrete sine-Gordon model at roots of 1: Integrable quantum system on the integrable classical background
• Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz
• The sigma model (dual) representation for a two-parameter family of integrable quantum field theories
• The integrable structure of nonrational conformal field theory
• Superconformal field theory and SUSY \(N=1\) KdV hierarchy. I: Vertex operators and Yang-Baxter equation.
• Quantization of soliton systems and Langlands duality
• The sine–Gordon model revisited: I
• Quantization of models with non-compact quantum group symmetry: modular XXZ magnet and lattice sinh-Gordon model
• Quantum Groups in Two-Dimensional Physics
• Serre presentations of Lie superalgebras
• Integrable structure of \(W_3\) conformal field theory, quantum Boussinesq theory and boundary affine Toda theory

This page was built for publication: Integrability of a family of quantum field theories related to sigma models