TY - JOUR
T1 - Separation of Variables in AdS/CFT:
T2 - functional Approach for the Fishnet CFT
AU - Cavaglia, Andrea
AU - Gromov, Nikolay
AU - Levkovich-Maslyuk, Fedor
PY - 2021/6
Y1 - 2021/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85110846062&partnerID=8YFLogxK
U2 - 10.1007/JHEP06(2021)131
DO - 10.1007/JHEP06(2021)131
M3 - Article
SN - 1029-8479
VL - 2021
SP - 1
EP - 74
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 6
M1 - 131
ER -