Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2512.07794 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917133112311808 |
|---|---|
| author | Bort, Josep Rubí Vera, Agustín Sabio Campillo, Eduardo Serna |
| author_facet | Bort, Josep Rubí Vera, Agustín Sabio Campillo, Eduardo Serna |
| contents | 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 $\mathbb{P}^1\setminus\{0,1,\infty\}$: $Ω(x) = -2\,dx/x - 4\,dx/(1-x)$, 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 $\mathcal{N}=4$ SYM and multi-Regge kinematics. The lattice thus isolates the algebraic core of BFKL evolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Knizhnik--Zamolodchikov structure of lattice BFKL evolution and the twist-two anomalous dimension Bort, Josep Rubí Vera, Agustín Sabio Campillo, Eduardo Serna High Energy Physics - Theory High Energy Physics - Phenomenology 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 $\mathbb{P}^1\setminus\{0,1,\infty\}$: $Ω(x) = -2\,dx/x - 4\,dx/(1-x)$, 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 $\mathcal{N}=4$ SYM and multi-Regge kinematics. The lattice thus isolates the algebraic core of BFKL evolution. |
| title | The Knizhnik--Zamolodchikov structure of lattice BFKL evolution and the twist-two anomalous dimension |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.07794 |