Abstract
We propose a broad class of d-dimensional conformal field theories of SU(N) adjoint scalar fields generalising the 4d Fishnet CFT (FCFT) discovered by Ö. Gürdogan and one of the authors as a special limit of γ-deformed \( \mathcal{N} \) = 4 SYM theory. In the planar N → ∞ limit the FCFTs are dominated by the “fishnet” planar Feynman graphs. These graphs are explicitly integrable, as was shown long ago by A. Zamolodchikov. The Zamolodchikov’s construction, based on the dual Baxter lattice (straight lines on the plane intersecting at arbitrary slopes) and the star-triangle identities, can serve as a “loom” for “weaving” the Feynman graphs of these FCFTs, with certain types of propagators, at any d. The Baxter lattice with M different slopes and any number of lines parallel to those, generates an FCFT consisting of M (M – 1) fields and a certain number of chiral vertices of different valences with distinguished couplings. These non-unitary, logarithmic CFTs enjoy certain reality properties for their spectrum due to a symmetry similar to the PT-invariance of non-hermitian hamiltonians proposed by C. Bender and S. Boettcher. We discuss in more detail the theories generated by a loom with M = 2, 3, 4, and the generalisation of the loom FCFTs for spinning fields in 4d.
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Acknowledgments
We would like to thank M. Alfimov, B. Basso, G. Ferrando, E. Trevisani and especially G. Korchemsky for discussions and comments. We appreciate the kind hospitality of the Kavli Institute for Theoretical Physics of the University of California Santa Barbara, where a part of this work has been done during the “Integrability in String, Field, and Condensed Matter Theory” 2022 program. This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. Research at the Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI.
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Kazakov, V., Olivucci, E. The loom for general fishnet CFTs. J. High Energ. Phys. 2023, 41 (2023). https://doi.org/10.1007/JHEP06(2023)041
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DOI: https://doi.org/10.1007/JHEP06(2023)041