Abstract
In this paper we consider systems of quantum particles in the 4d Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the Yang-Baxter equation in the unitary irreducibile representations of the principal series ∆ = 2 + iν for any left/right spins ℓ, \( \dot{\ell} \) of the particles. Such relations are interpreted in the language of Feynman diagrams as integral star-triangle identites between propagators of a conformal field theory. We prove the quantum integrability of a spin chain whose k-th site hosts a particle in the representation (∆k, ℓk, \( \dot{\ell} \)k) of the conformal group, realizing a spinning and inhomogeneous version of the quantum magnet used to describe the spectrum of the bi-scalar Fishnet theories [1]. For the special choice of particles in the scalar (1, 0, 0) and fermionic (3/2, 1, 0) representation the transfer matrices of the model are Bethe-Salpeter kernels for the double-scaling limit of specific two-point correlators in the γ-deformed \( \mathcal{N} \) = 4 and \( \mathcal{N} \) = 2 supersymmetric theories.
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Derkachov, S., Olivucci, E. Conformal quantum mechanics & the integrable spinning Fishnet. J. High Energ. Phys. 2021, 60 (2021). https://doi.org/10.1007/JHEP11(2021)060
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DOI: https://doi.org/10.1007/JHEP11(2021)060