Exact scattering amplitudes in conformal fishnet theory

Abstract

We compute the leading-color contribution to four-particle scattering amplitude in four-dimensional conformal fishnet theory that arises as a special limit of γ-deformed N = 4 SYM. We show that the single-trace partial amplitude is protected from quantum corrections whereas the double-trace partial amplitude is a nontrivial infrared finite function of the ratio of Mandelstam invariants. Applying the Lehmann-Symanzik-Zimmerman reduction procedure to the known expression of a four-point correlation function in the fishnet theory, we derive a new representation for this function that is valid for arbitrary coupling. We use this representation to find the asymptotic behavior of the double-trace amplitude in the high-energy limit and to compute the corresponding exact Regge trajectories. We verify that at weak coupling the expressions obtained are in agreement with an explicit five-loop calculation.

On the Regge limit of Fishnet correlators

“…Using Sommerfeld Watson transform as usually done in studying the Regge limit of QFT scattering amplitudes, we obtain the Regge poles of our correlator. This is presented in detail in section (3).…”

“…A LLA (s, t) ∝ log s , (1.8) 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. An immediate obstruction to generalizing their method to the 1 and 2-magnon cases is the fact that the 1 and 2-magnon states describe a bound state which is off-shell.…”

Twistor fishnets

“…Since the theory is invariant under φ 1 → (φ 1 ) T , φ 2 → (φ 2 ) T , it suffices to consider the former class. In [19] it was shown that A 4 (1, 1) is tree-level exact; let us review the argument here. Figure 4 displays the tree-level contributions to A 4 (1, 1) from the single trace vertex and the double trace vertices proportional to α 2 2 , as well as the 1-loop diagram which receives contributions from both of these single and double trace vertices.…”

“…Term-by-term, (5.21) is UV-divergent, but it is straightforward to see that the combination of all three terms is finite. This is the same mechanism that removes all divergences from the four-point single colour amplitudes (cf., [19]) at the conformal fixed point. On twistor space, the diagram corresponding to the first term in (5.21) evaluates to: at the conformal fixed point.…”

“…Anomalous dimensions, certain correlation functions and scattering amplitudes have all been determined exactly as functions of the coupling in FCFT [12,[18][19][20][21]. In addition, FCFT appears to admit a holographic description in terms of a discretized string-like model [22][23][24][25], and provides a first example of a non-supersymmetric 4d QFT with spontaneously broken conformal invariance [26].…”