Exact Correlation Functions in Conformal Fishnet Theory

Abstract

We compute exactly various 4-point correlation functions of shortest scalar operators in bi-scalar planar four-dimensional "fishnet" CFT. We apply the OPE to extract from these functions the exact expressions for the scaling dimensions and the structure constants of all exchanged operators with an arbitrary Lorentz spin. In particular, we determine the conformal data of the simplest unprotected two-magnon operator analogous to the Konishi operator, as well as of the one-magnon operator. We show that at weak coupling 4-point correlation functions can be systematically expanded in terms of harmonic polylogarithm functions and verify our results by explicit calculation of Feynman graphs at a few orders in the coupling. At strong coupling we obtain that the correlation functions exhibit the scaling behaviour typical for semiclassical description hinting at the existence of the holographic dual.

arXiv comment58 pages, some results in Mathematica format available in CodeForArxiv.m file attached

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Cited by in corpus (34)

• Harmonic Analysis and Mean Field Theory
• Bootstrapping the simplest correlator in planar N = 4 SYM at all loops
• Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
• Analytic Euclidean Bootstrap
• Detectors in weakly-coupled field theories
• Higher-Point Conformal Blocks in the Comb Channel
• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Thermodynamic Bethe Ansatz for Fishnet CFT
• Quantum Fishchain in $Ad{S}_5$
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Hexagons and Correlators in the Fishnet Theory
• New Methods for Conformal Correlation Functions
• Colour-Twist Operators I: Spectrum and Wave Functions
• The Holographic Dual of Strongly γ-deformed N=4 SYM Theory: Derivation, Generalization, Integrability and Discrete Reparametrization Symmetry
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• The Loom for General Fishnet CFTs
• Efficient Rules for All Conformal Blocks
• Conformal Regge Theory at Finite Boost
• The Integrable (Hyper)eclectic Spin Chain
• Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles
• Asymptotic freedom in a strongly interacting scalar quantum field theory in four Euclidean dimensions
• Twistor fishnets
• Instability of complex CFTs with operators in the principal series
• Combinatorial Solution of the Eclectic Spin Chain
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Checkerboard CFT
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Regge amplitudes in Generalized Fishnet and Chiral Fishnet Theories
• Correlation functions of determinant operators in conformal fishnet theory
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• A Large Twist Limit for Any Operator
• Anomalous dimensions at small spins
• The thermal representation of conformal ladder integrals
• BC-type open $SL(2,\mathbb{C})$ spin chain