## Abstract

We review the applications of the Quantum Spectral Curve (QSC) method to the Regge (BFKL) limit in N = 4 supersymmetric Yang-Mills theory. QSC, based on quantum integrability of the AdS5/CFT4 duality, was initially developed as a tool for the study of the spectrum of anomalous dimensions of local operators in the N = 4 SYM in the planar, Nc → ∞ limit. We explain how to apply the QSC for the BFKL limit, which requires non-trivial analytic continuation in spin S and extends the initial construction for non-local light-ray operators.We give a brief review of high precision non-perturbative numerical solutions and analytic perturbative data resulting from this approach. We also describe as a simple example of the QSC construction the leading order in the BFKL limit. We show that the QSC substantially simplifies in this limit and reduces to the Faddeev-Korchemsky Baxter equation for Q-functions. Finally, we review recent results for the Fishnet CFT, which carries a number of similarities with Lipatov’s integrable spin chain for interacting Reggeized gluons.

Original language | English |
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Title of host publication | From the Past to the Future |

Subtitle of host publication | The Legacy of Lev Lipatov |

Publisher | World Scientific Publishing Co. |

Pages | 335-367 |

Number of pages | 33 |

ISBN (Electronic) | 9789811231124 |

ISBN (Print) | 9789811231117 |

DOIs | |

Publication status | Published - 1 Jan 2021 |