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We introduce a D-dimensional conformal quantum field theory, generalizing a 4D model. This theory features fishnet Feynman graphs and an integrable spin chain, allowing exact calculations of operator dimensions and OPE constants.

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Area of Science:

  • Quantum Field Theory
  • High Energy Physics
  • String Theory

Background:

  • Introduces a D-dimensional generalization of a 4D biscalar conformal quantum field theory.
  • This theory is a strong-twist limit of γ-deformed N=4 supersymmetric Yang-Mills theory.
  • Planar correlators are conformal and dominated by fishnet Feynman graphs.

Purpose of the Study:

  • Generalize 4D results to any dimension D.
  • Compute a four-point correlation function exactly at any coupling.
  • Extract operator dimensions and operator product expansion (OPE) structure constants.

Main Methods:

  • Utilize a D-dimensional generalization of the 4D biscalar conformal quantum field theory.
  • Employ the integrable conformal SO(1,D+1) spin chain to describe graph dynamics.
  • Generalize 4D results for fishnet graph calculations to any dimension D.

Main Results:

  • The D-dimensional theory's planar correlators are conformal and dominated by fishnet graphs.
  • The dynamics are governed by an integrable conformal SO(1,D+1) spin chain.
  • Exact dimensions of operators with chiral charge 2 and any spin were extracted, along with OPE structure constants.

Conclusions:

  • The study provides an exact solution for a class of fishnet graphs in D dimensions.
  • The findings connect conformal field theory with integrable systems and quantum chromodynamics.
  • This work offers a framework for studying quantum field theories in higher dimensions.