2025/12/08 by Bort, Josep Rubí, Vera, Agustín Sabio, Campillo, Eduardo Serna
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Quantum chaos and dynamical systems #Quantum many-body systems
paper · doi:10.48550/arxiv.2512.07794
openalex publication_date 2025/12/08 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28
We study a lattice regularization of the BFKL evolution, showing its bulk dynamics is governed by an abelian Knizhnik--Zamolodchikov equation. The Hamiltonian combines long-range hopping with virtual corrections encoded by harmonic numbers. An exact walk expansion renders Reggeisation manifest at finite system size. In the bulk continuum limit, evolution reduces to a connection on ℙ1∖\0,1,∞\: Ω(x) = -2 dx/x - 4 dx/(1-x), with solutions in \0,1\-alphabet harmonic polylogarithms. Projecting to the collinear sector via Brown's single-valued map organizes the twist-two anomalous dimension's small-ω expansion, generating polynomials in odd zeta values, matching the transcendentality structure of planar N=4 SYM and multi-Regge kinematics. The lattice thus isolates the algebraic core of BFKL evolution.