Integrability and the spectrum of two-dimensional fishnet CFT

Abstract

A bstract : We formulate a closed set of equations for the spectrum of two-dimensional bi-scalar fishnet conformal field theory, comprising Baxter equations and quantisation conditions, which we derive operatorially from the underlying 𝔰𝔩(2) spin chain. These equations are reminiscent of the Quantum Spectral Curve framework found in other holographic conformal field theories and are expected to provide a complete non-perturbative description of the spectrum at arbitrary coupling. We solve our equations numerically at finite coupling and uncover a rich analytic structure, including state collisions and complex energy levels. Analytically, we introduce a new method to derive the Asymptotic Bethe Ansatz equations, which control the spectrum up to wrapping order and incorporate spinning states. We further extend our results to the twisted case, which may be particularly useful for future separation of variables analyses of correlation functions in this theory.

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BibTeX RIS

BibTeX

@article{ekhammar2026integrability,
  title = {{Integrability and the spectrum of two-dimensional fishnet CFT}},
  author = {Simon Ekhammar and Nikolay Gromov and Fedor Levkovich-Maslyuk and Paul Ryan},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)144},
  url = {https://link.springer.com/article/10.1007/JHEP10(2026)144},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Integrability and the spectrum of two-dimensional fishnet CFT
AU  - Simon Ekhammar
AU  - Nikolay Gromov
AU  - Fedor Levkovich-Maslyuk
AU  - Paul Ryan
PY  - 2026
DA  - 2026/10/14
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)144
UR  - https://link.springer.com/article/10.1007/JHEP10(2026)144
AB  - A bstract : We formulate a closed set of equations for the spectrum of two-dimensional bi-scalar fishnet conformal field theory, comprising Baxter equations and quantisation conditions, which we derive operatorially from the underlying 𝔰𝔩(2) spin chain. These equations are reminiscent of the Quantum Spectral Curve framework found in other holographic conformal field theories and are expected to provide a complete non-perturbative description of the spectrum at arbitrary coupling. We solve our equations numerically at finite coupling and uncover a rich analytic structure, including state collisions and complex energy levels. Analytically, we introduce a new method to derive the Asymptotic Bethe Ansatz equations, which control the spectrum up to wrapping order and incorporate spinning states. We further extend our results to the twisted case, which may be particularly useful for future separation of variables analyses of correlation functions in this theory.
SN  - 1029-8479
ER  -

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