Exact Scattering amplitudes in $\mathcal{N}=3$ supersymmetric Chern-Simons matter theory at large N


  Karthik Inbasekar  
Ben Gurion University

Chern-Simons matter theories are extremely interesting due to their diverse range of applications from condensed matter physics such as quantum hall effect to high energy physics in quantum gravity. When coupled to matter in the fundamental representations of $U(N), SU(N), O(N), Sp(N)$ the theory is exactly solvable in the 't Hooft large N limit. Moreover, there exist substantial evidence that these theories enjoy a strong-weak bosonization duality in the large N limit, while the finite N generalizations remain conjectural. Furthermore, Supersymmetric Chern-Simons matter theories are self-dual, and physical observables such as scattering amplitudes display remarkable simplicity and hidden symmetry structures such as dual superconformal symmetry and Yangian symmetry. Remarkably, the anyonic nature of the Chern-Simons interaction is visible in the singlet channel and is a conjectured universal feature of all Chern-Simons matter theories. In this talk, we describe our recent results on the exact scattering amplitudes in N=3 Chern-Simons matter theory. We set up the Dyson-Schwinger series for the four point correlation functions of scalar superfields in $\mathcal{N}=1$ superspace and solve for it exactly in the 't Hooft large N limit. We extract the exact four point scattering amplitude by taking the onshell limit of the correlator, we find that the scattering amplitude of the $\mathcal{N}=3$ theory in the large N limit is tree level exact, i.e all the loop corrections vanish. The result is very similar to that of the $\mathcal{N}=2$ Chern-Simons matter theories and several features such as dual superconformal symmetry and Yangian symmetry should follow. We hope that the methods used in this work may be exploited with suitable modifications to attempt to compute exact amplitudes in the $\mathcal{N}=6$ superconformal Chern-Simons matter theory or the Aharony-Bergmann-Jafferis-Maldacena (ABJM) which is a low energy description of M theory.