Type: Article
Publication Date: 2021-11-01
Citations: 7
DOI: https://doi.org/10.1007/jhep11(2021)204
A bstract In this paper we consider a conformal invariant chain of L sites in the unitary irreducible representations of the group SO(1 , 5). The k -th site of the chain is defined by a scaling dimension ∆ k and spin numbers $$ \frac{\ell_k}{2},\frac{\ell_k}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>,</mml:mo> <mml:mfrac> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> The model with open and fixed boundaries is shown to be integrable at the quantum level and its spectrum and eigenfunctions are obtained by separation of variables. The transfer matrices of the chain are graph-builder operators for the spinning and inhomogeneous generalization of squared-lattice “fishnet” integrals on the disk. As such, their eigenfunctions are used to diagonalize the mirror channel of the Feynman diagrams of Fishnet conformal field theories. The separated variables are interpreted as momentum and bound-state index of the mirror excitations of the lattice: particles with SO(4) internal symmetry that scatter according to an integrable factorized $$ \mathcal{S} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> -matrix in (1 + 1) dimensions