4 Citations (Scopus)


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 languageEnglish
Title of host publicationFrom the Past to the Future
Subtitle of host publicationThe Legacy of Lev Lipatov
PublisherWorld Scientific Publishing Co.
Number of pages33
ISBN (Electronic)9789811231124
ISBN (Print)9789811231117
Publication statusPublished - 1 Jan 2021


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