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Register a new userBasso-Dixon Correlators in Two-Dimensional Fishnet CFT
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We compute explicitly the two-dimensional version of Basso-Dixon type integrals for the planar four-point correlation functions given by conformal fishnet Feynman graphs. These diagrams are represented by a fragment of a regular square lattice of power-like propagators, arising in the recently proposed integrable bi-scalar fishnet CFT. The formula is derived from first principles, using the formalism of separated variables in integrable SL(2,C) spin chain. It is generalized to anisotropic fishnet, with different powers for propagators in two directions of the lattice.
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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.
We compute three-point correlation functions in the near-extremal, near-horizon region of a Kerr black hole, and compare to the corresponding finite-temperature conformal field theory correlators. For simplicity, we focus on scalar fields dual to operators ${cal O}_h$ whose conformal dimensions obey $h_3=h_1+h_2$, which we name emph{extremal} in analogy with the classic $AdS_5 times S^5$ three-point function in the literature. For such extremal correlators we find perfect agreement with the conformal field theory side, provided that the coupling of the cubic interaction contains a vanishing prefactor $propto h_3-h_1-h_2$. In fact, the bulk three-point function integral for such extremal correlators diverges as $1/(h_3-h_1-h_2)$. This behavior is analogous to what was found in the context of extremal AdS/CFT three-point correlators. As in AdS/CFT our correlation function can nevertheless be computed via analytic continuation from the non-extremal case.
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