# Small $x$ behavior in QCD from maximal entanglement and conformal invariance

## TL;DR

This paper links small-x QCD behavior to conformal field theory, showing that the entanglement entropy and structure function depend on the central charge, which is found to be 1, predicting a specific x-dependence for future experiments.

## Contribution

It introduces a conformal field theory approach to small-x QCD, deriving the central charge using Bethe Ansatz methods, and predicts a testable x-dependence of the structure function.

## Key findings

- Central charge c=1 for the conformal field theory describing small-x QCD.
- Predicts a structure function behavior of approximately x^{-1/3} at small x.
- Provides a theoretical framework connecting entanglement, conformal invariance, and QCD evolution.

## 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 (BFKL) 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 $\sim x^{-1/3}$ small $x$ behavior for the structure function -- the prediction that can be tested at the forthcoming Electron-Ion Collider.