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Small-x behavior in QCD from maximal entanglement and conformal invariance

Sebastian Grieninger1,2,*, Kun Hao3,4,†, Dmitri E. Kharzeev1,2,5,‡, and Vladimir Korepin2,6,§

  • *Contact author: sebastian.grieninger@stonybrook.edu
  • †Contact author: haoke72@163.com
  • ‡Contact author: dmitri.kharzeev@stonybrook.edu
  • §Contact author: vladimir.korepin@stonybrook.edu
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Phys. Rev. D 113, 094030 – Published 22 May, 2026

DOI: https://doi.org/10.1103/fvfm-hxpk

Abstract

Recent evidence suggests that, at small Bjorken x, QCD evolution drives the proton into a state of maximal entanglement. If the evolution kernel is assumed to be conformally invariant—as is the case for the Balitsky-Fadin-Kuraev-Lipatov equation—we can describe it by a conformal field theory. Moreover, the central charge c of the corresponding conformal field theory emerges as the key parameter governing the x dependence of both the entanglement entropy and the structure function. Here we apply the exact Bethe ansatz methods to the quantum spin chain dual to Lipatov’s high energy effective action to extract the central charge of the theory, and find that c=1. This implies the ∼x−1/3 small x behavior for the structure function—the prediction that can be tested at the forthcoming Electron-Ion Collider.

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Phys. Rev. D 113, 094030– Published 22 May, 2026
  • Received 11 September 2025
  • Accepted 21 April 2026
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