Integrable fishnet from γ-deformed N = 2 quivers

115

In our previous paper we derived the holographic dual of the planar fishnet CFT in four dimensions. The dual model becomes classical in the strongly coupled regime of the CFT and takes the form of an integrable chain of particles in five dimensions. Here we study the theory at the quantum level. By applying the canonical quantization procedure with constraints, we show that the model describes a quantum chain of particles propagating in AdS 5 . We prove the duality at the full quantum level in the u(1) sector and reproduce exactly the spectrum for the cases when it is known analytically.In particular, the graph building operator is self-adjoint with respect to this norm. Given the wave function ϕ O we can compute any correlation function of the operator O. For example, the two point function is given by5) 1 Here we have suppressed double trace interactions which are not relevant non-perturbatively [5, 10]. 2 Not to be confused with the 't Hooft coupling of the parent N = 4 SYM theory, λ. 3 When taking the conjugate of the wave function in (2.4), one does not conjugate the 't Hooft coupling ξ 2 . This relation is a straight forward generalization of the J = 2 case considered in [3] to any length.12 The extra polynomial factors in T's can be removed by the gauge transformation g(u) = e πu 2 Γ(−iu). Under the gauge transformationT1(u),T 1 (u) → u J ,T 6 (u) →T 6 (u)/u J andT4(u) →T4(u)/ u 2 + 1 4ξ 2 J whereas T 4 (u) does not change. The Q-operator transforms as Q(u) → g(u)Q(u).

Section: Discussionmentioning

confidence: 99%

Quantum fishchain in AdS5

Gromov

Sever

2019

115

“…These include fishnet theories in general dimensions [24], chiral fishnet theories [25], fishnet theory obtained from four-dimensional N = 2 quiver gauge theories [26]. Similar analysis can be undertaken for the double scaling limit of γ-twisted ABJM theories considered in [27].…”

Section: Discussionmentioning

confidence: 99%

“…dν e iλν Γ(2iν)Γ −iν − t 2 + 2 Γ(iν) 2 (C. 26) where we have defined, λ = log L. Note that as L → ∞ so does λ i.e, λ → ∞ however at a much slower rate. We can do this integral by parts repeatedly.…”

mentioning

confidence: 99%

On the Regge limit of Fishnet correlators

Chowdhury

Haldar

Sen

2019

We study the Regge trajectories of the Mellin amplitudes of the 0−, 1− and 2− magnon correlators of the Fishnet theory. Since fishnet theory is both integrable and conformal, the correlation functions are known exactly. We find that while for 0 and 1 magnon correlators, the Regge poles can be exactly determined as a function of coupling, 2-magnon correlators can only be dealt with perturbatively. We evaluate the resulting Mellin amplitudes at weak coupling, while for strong coupling we do an order of magnitude calculation. II Superstring theory [5], the Regge limit of the scattering amplitude scales as s 2+ α t 2 which denotes graviton dominance in the high energy limit (t is negative). Similarly for QCD, one can see from [6] that the LLA (leading log approximation) contribution to the Regge limit comes from,(1.5)The same can be shown in a perturbative manner for the N = 4 SYM [7] for which in weak coupling,In contrast, for the fishnet theories under consideration, we find that for the 0, 1, 2−magnon cases, in the weak coupling, the leading Regge theory is dominated by,respectively. This is expected to be connected with the inherent non-unitarity of the theory so that the effective exchanges in the Regge limit has negative spins. In this case, the LLA contribution is expected 1 Unlike other theories, where the Regge trajectories are only known in certain limits (say the weak coupling limit), here the trajectories are exact functions of the coupling ξ.

“…From the integrability point of view, the rotation by θ corresponds to twisting a boundary condition. It is then interesting to consider an analogue of the "fishnet" limit [207][208][209][210]; namely the double-scaling limit in which the twist angle goes to i∞ while λ goes to zero keeping a product λe −iθ fixed. In our setup, this would correspond to the famous BFKL limit.…”

Section: Regge and Bfkl Limit And Light-ray Operatorsmentioning

confidence: 99%

Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function

Jiang

Komatsu

Vescovi

2020

173

We develop a novel nonperturbative approach to a class of three-point functions in planar N = 4 SYM based on Thermodynamic Bethe Ansatz (TBA). More specifically, we study three-point functions of a non-BPS single-trace operator and two determinant operators dual to maximal Giant Graviton D-branes in AdS 5 ×S 5. They correspond to disk one-point functions on the worldsheet and admit a simpler and more powerful integrability description than the standard single-trace three-point functions. We first introduce two new methods to efficiently compute such correlators at weak coupling; one based on large N collective fields, which provides an example of open-closed-open duality discussed by Gopakumar, and the other based on combinatorics. The results so obtained exhibit a simple determinant structure and indicate that the correlator can be interpreted as a generalization of g-functions in 2d QFT; an overlap between an integrable boundary state and a state corresponding to the single-trace operator. We then determine the boundary state at finite coupling using the symmetry, the crossing equation and the boundary Yang-Baxter equation. With the resulting boundary state, we derive the ground-state g-function based on TBA and conjecture its generalization to other states. This is the first fully nonperturbative proposal for the structure constants of operators of finite length. The results are tested extensively at weak and strong couplings. Finally, we point out that determinant operators can provide better probes of sub-AdS locality than single-trace operators and discuss possible applications.