Bi-scalar integrable CFT at any dimension

Abstract

We propose a $D$-dimensional generalization of $4D$ bi-scalar conformal quantum field theory recently introduced by Gürdogan and one of the authors as a strong-twist double scaling limit of $\gamma$-deformed $\mathcal{N}=4$ SYM theory. Similarly to the $4D$ case, this D-dimensional CFT is also dominated by "fishnet" Feynman graphs and is integrable in the planar limit. The dynamics of these graphs is described by the integrable conformal $SO(D+1,1)$ spin chain. In $2D$ it is the analogue of L. Lipatov's $SL(2,\mathbb{C})$ spin chain for the Regge limit of $QCD$, but with the spins $s=1/4$ instead of $s=0$. Generalizing recent $4D$ results of Grabner, Gromov, Korchemsky and one of the authors to any $D$ we compute exactly, at any coupling, a four point correlation function, dominated by the simplest fishnet graphs of cylindric topology, and extract from it exact dimensions of R-charge 2 operators with any spin and some of their OPE structure constants.

5 pages, 4 figures, v2: typos corrected, v3: as accepted for publication on Physical Review Letters

References in corpus (5)

• All point correlation functions in SYK
• Strongly γ-deformed N=4 SYM as an integrable CFT
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Massless two-loop self-energy diagram: Historical review

Cited by in corpus (49)

• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
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• Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
• Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties
• Exact Correlation Functions in Conformal Fishnet Theory
• Exactly solvable magnet of conformal spins in four dimensions
• Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT${}_4$
• 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
• Continuum limit of fishnet graphs and AdS sigma model
• Separation of variables for rational gl(n) spin chains in any compact representation, via fusion, embedding morphism and Backlund flow
• Quantum Fishchain in $Ad{S}_5$
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Hexagons and Correlators in the Fishnet Theory
• Spontaneous Conformal Symmetry Breaking in Fishnet CFT
• Massive Fishnets
• The One-Loop Spectral Problem of Strongly Twisted $\mathcal{N}$=4 Super Yang-Mills Theory
• The Loom for General Fishnet CFTs
• Conformal graphs as twisted partition functions
• The F-theorem in the melonic limit
• Conformal Symmetry and Composite Operators in the $O(N{)}^3$ Tensor Field Theory
• 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
• Hexagonalization of Fishnet integrals I: mirror excitations
• Twistor fishnets
• Instability of complex CFTs with operators in the principal series
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Conformal Triangles and Zig-Zag Diagrams
• Checkerboard CFT
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• N=4 SYM Quantum Spectral Curve in BFKL regime
• Mellin$-$Barnes Transformation for Two-Loop Master-Diagram
• Conformal quantum mechanics & the integrable spinning Fishnet
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Regge amplitudes in Generalized Fishnet and Chiral Fishnet Theories
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• On analytical perturbative solution of ABJM quantum spectral curve
• The Feyn-Structure of Yangian Symmetry
• Non-Local Symmetries of Planar Feynman Integrals
• On the Regge limit of Fishnet correlators
• The thermal representation of conformal ladder integrals
• Dual Conformal Symmetry and Iterative Integrals in Six Dimensions
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions
• Canonical Quantization of Noncompact Spin System
• BC-type open $SL(2,\mathbb{C})$ spin chain