Abstract
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.
Highlights
N = 4 SYM is one of the few most convenient playground for analyzing the scattering amplitudes for a CFT, since in addition to conformal symmetries, it admits a Lagrangian description
We study the Regge trajectories of the Mellin amplitudes of the 0,1- and 2-magnon correlators of the Fishnet theory
We evaluate the resulting Mellin amplitudes at weak coupling, while for strong coupling we do an order of magnitude calculation
Summary
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 to come effectively from the 0-magnon graphs, in a simple form, ALLA(s, t) ∝ log s ,. In [3], the author studies the Regge limit of the 0-magnon four point amplitude in the fishnet theory using standard LSZ reduction techniques in momentum space. 1-magnon state XZ(x) after a Fourier transform describes a twoparticle state that cannot be on-shell Another way to see this is to verify that 4-point correlator Tr[XZ(x1)X(x2)]Tr[X Z(x3)X (x4)] in the momentum space does not have a pole at p21 = 0 and p23 = 0 (but it does have poles at p22 = 0 and p24 = 0) and, the LSZ reduction gives a vanishing result.
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