Basso-Dixon Correlators in Two-Dimensional Fishnet CFT

Abstract

We compute explicitly the two-dimensional version of Basso-Dixon type integrals for the planar four-point correlation functions given by conformal fishnet Feynman graphs. These diagrams are represented by a fragment of a regular square lattice of power-like propagators, arising in the recently proposed integrable bi-scalar fishnet CFT. The formula is derived from first principles, using the formalism of separated variables in integrable SL(2,C) spin chain. It is generalized to anisotropic fishnet, with different powers for propagators in two directions of the lattice.

arXiv comment30 pages, 13 figures, v2: improved formulas, typos corrected

References in corpus (41)

• Review of AdS/CFT Integrability: An Overview
• Separation of Variables. New Trends.
• How Algebraic Bethe Ansatz works for integrable model
• High energy QCD as a completely integrable model
• Quantum spectral curve for AdS_5/CFT_4
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Quantum Inverse Scattering Method. Selected Topics
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Gluing Ladders into Fishnets
• Perturbative Search for Fixed Lines in Large N Gauge Theories
• Strongly γ-deformed N=4 SYM as an integrable CFT
• Integrability of Conformal Fishnet Theory
• Yangian Symmetry for Fishnet Feynman Graphs
• Integrability of scattering amplitudes in N=4 SUSY
• Effective potential in non-supersymmetric SU(N) x SU(N) gauge theory and interactions of type 0 D3-branes
• Bi-scalar integrable CFT at any dimension
• Conformal algebra: R-matrix and star-triangle relation
• Yangian Symmetry for Bi-Scalar Loop Amplitudes
• TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
• Towards multiple elliptic polylogarithms
• Elliptic Polylogarithms and Basic Hypergeometric Functions
• On a CFT limit of planar ${\gamma }_i$-deformed $\mathcal{N}=4$ SYM theory
• Non-conformality of gamma_i-deformed N=4 SYM theory
• Conformal bootstrap for the BFKL Pomeron
• On quantum separation of variables
• Quantum mechanics of null polygonal Wilson loops
• Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• Continuum limit of fishnet graphs and AdS sigma model
• A piece of cake: the ground-state energies in gamma_i-deformed N=4 SYM theory
• Three-point correlator of twist-2 operators in BFKL limit
• Iterative construction of eigenfunctions of the monodromy matrix for SL(2,C) magnet
• Integrable spin chains and scattering amplitudes
• Unitarity of the SoV transform for the Toda chain
• Operator approach to analytical evaluation of Feynman diagrams
• Separation of variables for the quantum SL(3,C) spin magnet: eigenfunctions of Sklyanin B-operator
• Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs
• On $b$-Whittaker functions

Cited by in corpus (42)

• Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties
• Exactly solvable magnet of conformal spins in four dimensions
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• 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
• Thermodynamic Bethe Ansatz for Fishnet CFT
• Separation of variables for rational gl(n) spin chains in any compact representation, via fusion, embedding morphism and Backlund flow
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Hexagons and Correlators in the Fishnet Theory
• Yangian Bootstrap for Massive Feynman Integrals
• Spontaneous Conformal Symmetry Breaking in Fishnet CFT
• On Complex Gamma-Function Integrals
• The Holographic Dual of Strongly γ-deformed N=4 SYM Theory: Derivation, Generalization, Integrability and Discrete Reparametrization Symmetry
• The One-Loop Spectral Problem of Strongly Twisted $\mathcal{N}$=4 Super Yang-Mills Theory
• Decagon at Two Loops
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Mirror channel eigenvectors of the $d$-dimensional fishnets
• The Loom for General Fishnet CFTs
• Conformal graphs as twisted partition functions
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Form-factors and complete basis of observables via separation of variables for higher rank spin chains
• Integrability for Feynman Integrals
• Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles
• Twistor fishnets
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Conformal Triangles and Zig-Zag Diagrams
• N=4 SYM Quantum Spectral Curve in BFKL regime
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Checkerboard CFT
• Mellin$-$Barnes Transformation for Two-Loop Master-Diagram
• Conformal quantum mechanics & the integrable spinning Fishnet
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Light-cone limits of large rectangular fishnets
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• Separation of variables for higher rank integrable models: review of recent progress
• The thermal representation of conformal ladder integrals
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions
• The Gelfand-Tsetlin basis for infinite-dimensional representations of $g{l}_n(\mathbb{C})$
• BC-type open $SL(2,\mathbb{C})$ spin chain