Small $x$ behavior in QCD from maximal entanglement and conformal invariance
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914595322462208 |
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| author | Grieninger, Sebastian Hao, Kun Kharzeev, Dmitri E. Korepin, Vladimir |
| author_facet | Grieninger, Sebastian Hao, Kun Kharzeev, Dmitri E. Korepin, Vladimir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Small $x$ behavior in QCD from maximal entanglement and conformal invariance Grieninger, Sebastian Hao, Kun Kharzeev, Dmitri E. Korepin, Vladimir High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Experiment Nuclear Theory Quantum Physics 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. |
| title | Small $x$ behavior in QCD from maximal entanglement and conformal invariance |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Experiment Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2508.21643 |