Dual Separated Variables and Scalar Products

Abstract

Separation of variables (SoV) is an extremely efficient and elegant technique for analysing physical systems but its application to integrable spin chains was limited until recently to the simplest su(2) cases. In this paper we continue developing the SoV program for higher-rank spin chains and demonstrate how to derive the measure for the su(3) case. Our results are a natural consequence of factorisability of the wave function and functional orthogonality relations following from the interplay between Baxter equations for Q-functions and their dual.

arXiv comment6 pages; v2: typos fixed, published version

References in corpus (12)

• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Quantum Integrable Systems and Elliptic Solutions of Classical Discrete Nonlinear Equations
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Separation of Variables in the Classical Integrable SL(3) Magnetic Chain
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)]
• Quark--anti-quark potential in N=4 SYM
• On quantum separation of variables
• Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame
• Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$

Cited by in corpus (28)

• Exactly solvable magnet of conformal spins in four dimensions
• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Thermodynamic Bethe Ansatz for Fishnet CFT
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• A review of the AdS/CFT Quantum Spectral Curve
• Mirror channel eigenvectors of the $d$-dimensional fishnets
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• Functional Equations and Separation of Variables for Exact g-Function
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Form-factors and complete basis of observables via separation of variables for higher rank spin chains
• Correlation functions by Separation of Variables: the XXX spin chain
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
• Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb{R})$ Spin Chains
• Conformal quantum mechanics & the integrable spinning Fishnet
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Correlation functions of determinant operators in conformal fishnet theory
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Norms and scalar products for AdS_3
• Separation of variables for higher rank integrable models: review of recent progress
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint