Basso-Dixon correlators in two-dimensional fishnet CFT

Recently, we constructed the first-principle derivation of the holographic dual of N = 4 SYM in the double-scaled γ-deformed limit directly from the CFT side. The dual fishchain model is a novel integrable chain of particles in AdS 5 . It can be viewed as a discretized string and revives earlier string-bit approaches. The original derivation was restricted to the operators built out of one of two types of scalar fields. In this paper, we extend our results to the general operators having any number of scalars of both types, except for a very special case when their numbers are equal. Interestingly, the extended model reveals a new discrete reparametrization symmetry of the "world-sheet", preserving all integrals of motion. We use integrability to formulate a closed system of equations, which allows us to solve for the spectrum of the model in full generality, and present non-perturbative numerical results. We show that our results are in agreement with the Asymptotic Bethe Ansatz of the fishnet model up to the wrapping order at weak coupling.

Section: Resultsmentioning

confidence: 92%

The holographic dual of strongly γ-deformed $$ \mathcal{N} $$ = 4 SYM theory: derivation, generalization, integrability and discrete reparametrization symmetry

Gromov

Sever

2020

“…These form factors are analogous to the 3-point correlators of the type xOOLy in the fishnet theory or N " 4 super Yang-Mills, where L is a marginal operator such as the Lagrangian insertion 21 and O is a non-trivial single trace operator. SoV-type expressions for such structure constants, and even more general ones, have already been found in different parameter limits of N " 4 SYM in a growing number of cases [50,51,[67][68][69] 22 , giving strong indications of the viability of a SoV strategy for correlators. Generalization of our construction should give a closed totally non-perturbative expression for such 3-point correlator in terms of Q-functions, which are known from the Quantum Spectral Curve method developed in [71,72], see [34,35] for reviews.…”

Section: Discussionmentioning

confidence: 99%

Separation of variables and scalar products at any rank

Cavaglià

Gromov

Levkovich-Maslyuk

2019

109

Separation of variables (SoV) is a special property of integrable models which ensures that the wavefunction has a very simple factorised form in a specially designed basis. Even though the factorisation of the wavefunction was recently established for higher rank models by two of the authors and G. Sizov, the measure for the scalar product was not known beyond the case of rank one symmetry. In this paper we show how this measure can be found, bypassing an explicit SoV construction. A key new observation is that the measure for spin chains in a highest-weight infinite dimensional representation of slpN q couples Qfunctions at different nesting levels in a non-symmetric fashion. We also managed to express a large number of form factors as ratios of determinants in our new approach. We expect our method to be applicable in a much wider setup including the problem of computing correlators in integrable CFTs such as the fishnet theory, N " 4 SYM and the ABJM model.

“…The generalization of bi-scalar fishnet CFT to any dimension D [21] poses a natural question whether the D-dimensional generalization of the full 3-coupling χCFT exists. A related question: can we generalize the Basso-Dixon type fishnet integrals -the four-point single-trace correlators of scalar fields in bi-scalar CFT -explicitly computed in D = 4 [55] and D = 2 [56], to the case of dynamical fishnets of χCFT?…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Generalized fishnets and exact four-point correlators in chiral CFT4

Казаков

Olivucci

Preti

2019

Self Cite

102

We study the Feynman graph structure and compute certain exact four-point correlation functions in chiral CFT 4 proposed byÖ. Gürdogan and one of the authors as a double scaling limit of γ-deformed N = 4 SYM theory. We give full description of bulk behavior of large Feynman graphs: it shows a generalized "dynamical fishnet" structure, with a dynamical exchange of bosonic and Yukawa couplings. We compute certain fourpoint correlators in the full chiral CFT 4 , generalizing recent results for a particular onecoupling version of this theory -the bi-scalar "fishnet" CFT. We sum up exactly the corresponding Feynman diagrams, including both bosonic and fermionic loops, by Bethe-Salpeter method. This provides explicit OPE data for various twist-2 operators with spin, showing a rich analytic structure, both in coordinate and coupling spaces.