Cutting the cylinder into squares: The square form factor

Abstract

In this article we present a method for constructing two-point functions in the spirit of the hexagon proposal, which leads us to propose a "square form factor". Since cutting the square gives us two squares, we can write a consistency condition that heavily constrains such form factors. In particular, we are able to use this constraint to reconstruct the Gaudin through the forest expansion of the determinant appearing in its definition. We also use this procedure to compute the norm of off-shell Bethe states for some simple cases.

arXiv comment34 pages, 10 figures

References in corpus (29)

• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Quantum spectral curve for AdS_5/CFT_4
• Tailoring Three-Point Functions and Integrability
• Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• Hexagonalization of Correlation Functions
• Tessellating cushions: four-point functions in N=4 SYM
• Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4
• Exact form factors in integrable quantum field theories: the sine-Gordon model (II)
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Three-Point Functions in N=4 SYM Theory at One-Loop
• Yang-Mills Correlation Functions from Integrable Spin Chains
• Quantum spectral curve as a tool for a perturbative quantum field theory
• Structure constants at wrapping order
• Fast analytic solver of rational Bethe equations
• Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Twist-2 at seven loops in planar N=4 SYM theory: Full result and analytic properties
• Towards a string bit formulation of N=4 super Yang-Mills
• Worldsheet Form Factors in AdS/CFT
• Bethe Ansaetze for GKP strings
• From the octagon to the SFT vertex - gluing and multiple wrapping
• String Bits and the Spin Vertex
• Diagonal form factors and hexagon form factors
• Fermionic Correlators from Integrability
• Structure constants of operators on the Wilson loop from integrability
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• Vertex operators for quantum groups and application to integrable systems

Cited by in corpus (2)

• A study of integrable form factors in massless relativistic AdS_3
• A study of integrable form factors in massless relativistic $Ad{S}_2$