Hexagonalization of Fishnet integrals I: mirror excitations

Abstract

In this paper we consider a conformal invariant chain of $L$ sites in the unitary irreducible representations of the group $SO(1,5)$. The $k$-th site of the chain is defined by a scaling dimension ${\Delta }_k$ and spin numbers $\frac{{\ell }_k}{2}$, $\frac{{\dot{\ell }}_k}{2}$. The model with open and fixed boundaries is shown to be integrable at the quantum level and its spectrum and eigenfunctions are obtained by separation of variables. The transfer matrices of the chain are graph-builder operators for the spinning and inhomogeneous generalization of squared-lattice "fishnet" integrals on the disk. As such, their eigenfunctions are used to diagonalize the mirror channel of the the Feynman diagrams of Fishnet conformal field theories. The separated variables are interpreted as momentum and bound-state index of the $\text{mirror excitations}$ of the lattice: particles with $SO(4)$ internal symmetry that scatter according to an integrable factorized $\mathcal{S}$-matrix in $(1+1)$ dimensions.

arXiv commentv2: minor corrections. 45 pages, 42 figures, 6 appendices

References in corpus (43)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Review of AdS/CFT Integrability: An Overview
• Quantum Inverse Scattering Method and Correlation Functions
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Separation of Variables. New Trends.
• How Algebraic Bethe Ansatz works for integrable model
• Lax Pair for Strings in Lunin-Maldacena Background
• Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Hexagonalization of Correlation Functions
• Tessellating cushions: four-point functions in N=4 SYM
• Gluing Ladders into Fishnets
• Strongly γ-deformed N=4 SYM as an integrable CFT
• Bootstrapping the simplest correlator in planar N = 4 SYM at all loops
• Integrability of Conformal Fishnet Theory
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Yangian Symmetry for Fishnet Feynman Graphs
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Bi-scalar integrable CFT at any dimension
• Conformal algebra: R-matrix and star-triangle relation
• Yangian Symmetry for Bi-Scalar Loop Amplitudes
• Yangian Bootstrap for Conformal Feynman Integrals
• On a CFT limit of planar ${\gamma }_i$-deformed $\mathcal{N}=4$ SYM theory
• Exactly solvable magnet of conformal spins in four dimensions
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT${}_4$
• Separation of variables and scalar products at any rank
• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Integrable Fishnet from $\gamma$-Deformed $\mathcal{N}=2$ Quivers
• Thermodynamic Bethe Ansatz for Fishnet CFT
• The Octagon as a Determinant
• Form factors of integrable Heisenberg (higher) spin chains
• A piece of cake: the ground-state energies in gamma_i-deformed N=4 SYM theory
• Separation of variables for rational gl(n) spin chains in any compact representation, via fusion, embedding morphism and Backlund flow
• Lectures on S-matrices and Integrability
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Hexagons and Correlators in the Fishnet Theory
• Iterative construction of eigenfunctions of the monodromy matrix for SL(2,C) magnet
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• Decagon at Two Loops
• Spinorial R-matrix
• Minkowski Box from Yangian Bootstrap

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• BC-type open $SL(2,\mathbb{C})$ spin chain