Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$

Abstract

In this paper we study a wide class of planar single-trace four point correlators in the chiral conformal field theory ($\chi$CFT${}_4$) arising as a double scaling limit of the $\gamma$-deformed $\mathcal{N}=4$ SYM theory. In the planar (t'Hooft) limit, each of such correlators is described by a single Feynman integral having the bulk topology of a square lattice "fishnet" and/or of an honeycomb lattice of Yukawa vertices. The computation of this class of Feynmann integrals at any loop is achieved by means of an exactly-solvable spin chain magnet with $SO(1,5)$ symmetry. In this paper we explain in detail the solution of the magnet model as presented in our recent letter and we obtain a general formula for the representation of the Feynman integrals over the spectrum of the separated variables of the magnet, for any number of scalar and fermionic fields in the corresponding correlator. For the particular choice of scalar fields only, our formula reproduces the conjecture of B. Basso and L. Dixon for the fishnet integrals.

arXiv comment80 pages, 52 figures. v2: references added

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• Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
• Yangian Bootstrap for Massive Feynman Integrals
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Mirror channel eigenvectors of the $d$-dimensional fishnets
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• Form-factors and complete basis of observables via separation of variables for higher rank spin chains
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• Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles
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• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Checkerboard CFT
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Light-cone limits of large rectangular fishnets
• Antipodal self-duality of square fishnet graphs
• Correlation functions of determinant operators in conformal fishnet theory
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• BC-type open $SL(2,\mathbb{C})$ spin chain