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Separation of Variables in AdS/CFT: functional Approach for the Fishnet CFT

Research output: Contribution to journalArticlepeer-review

Andrea Cavaglia, Nikolay Gromov, Fedor Levkovich-Maslyuk

Original languageEnglish
Article number131
Pages (from-to)1-74
JournalJournal of High Energy Physics
Issue number6
Early online date21 Jun 2021
Accepted/In press9 Jun 2021
E-pub ahead of print21 Jun 2021
PublishedJun 2021


King's Authors


The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in N = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of N = 4 SYM – the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the N = 4 SYM case, as we speculate in the last part of the article.

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