Abstract
We propose a D-dimensional generalization of 4D biscalar conformal quantum field theory recently introduced by Gürdogan and one of the authors as a particular strong-twist limit of γ-deformed N=4 supersymmetric Yang-Mills theory. Similar to the 4D case, the planar correlators of this D-dimensional theory are conformal and dominated by "fishnet" Feynman graphs. The dynamics of these graphs is described by the integrable conformal SO(1,D+1) spin chain. In 2D, it is the analogue of Lipatov's SL(2,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 operators with chiral charge 2 and any spin together with some of their operator product expansion structure constants.
Highlights
Introduction.—Conformal field theories (CFTs) are ubiquitous in two dimensions [1], and quite a few supersymmetric CFTs in D 1⁄4 3, 4, 6 dimensions are known
That is why a new family of planar integrable CFTs obtained in Ref. [5] as a special double-scaling limit of γ-deformed N 1⁄4 4 supersymmetric Yang-Mills (SYM) theory seems to be an important and instructive example
This theory can be studied via quantum spectral curve (QSC) formalism [6,7,8] or using the integrability of its dominant Feynman graphs via the conformal SUð2; 2Þ noncompact spin chain
Summary
We propose a D-dimensional generalization of 4D biscalar conformal quantum field theory recently introduced by Gürdogan and one of the authors as a particular strong-twist limit of γ-deformed N 1⁄4 4 supersymmetric Yang-Mills theory. Similar to the 4D case, the planar correlators of this D-dimensional theory are conformal and dominated by “fishnet” Feynman graphs. [5] as a special double-scaling limit of γ-deformed N 1⁄4 4 SYM theory seems to be an important and instructive example This theory can be studied via quantum spectral curve (QSC) formalism [6,7,8] or using the integrability of its dominant Feynman graphs via the conformal SUð2; 2Þ noncompact spin chain. The nonlocal (for general D, ω) operators in kinetic terms should be understood as an integral kernel ð∂
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