Abstract
We present a basis of eigenvectors for the graph building operators acting along the mirror channel of planar fishnet Feynman integrals in d-dimensions. The eigenvectors of a fishnet lattice of length N depend on a set of N quantum numbers (uk , lk ), each associated with the rapidity and bound-state index of a lattice excitation. Each excitation is a particle in (1 + 1)-dimensions with O(d) internal symmetry, and the wave-functions are formally constructed with a set of creation/annihilation operators that satisfy the corresponding Zamolodchikovs-Faddeev algebra. These properties are proved via the representation, new to our knowledge, of the matrix elements of the fused R-matrix with O(d) symmetry as integral operators on the functions of two spacetime points. The spectral decomposition of a fishnet integral we achieved can be applied to the computation of Basso-Dixon integrals in higher dimensions.
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Derkachov, S., Ferrando, G. & Olivucci, E. Mirror channel eigenvectors of the d-dimensional fishnets. J. High Energ. Phys. 2021, 174 (2021). https://doi.org/10.1007/JHEP12(2021)174
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DOI: https://doi.org/10.1007/JHEP12(2021)174